2013-2014 UCS Geometry SEMESTER 1 REVIEW …macomb.k12.mi.us/utica/Eppler/media/13-14 Mid-Term...

2013-2014 UCS Geometry SEMESTER 1 REVIEW GUIDE #1 1 Jen and Beth are graphing triangles on this

coordinate grid. Beth graphed her triangle as shown. Jen must now graph the reflection of Beth’s triangle over the x-axis.

A

C

B

D

3 Find the new coordinates of when it is

rotated 90 clockwise about the origin.

A M’ (-2, 1), Q’ (-6, 1), H’ (-4, 5)

B M’ (2, -1), Q’ (6, -1), H’ (4, -5)

C M’ (5, 4), Q’ (-1, 6), H’ (-2, 1)

D M’ (8, 7), Q’ (8, 3), H’ (5, 4)

2 Trapezoid is drawn on the coordinate grid.

If you reflect the trapezoid over the dashed line, what would be the new coordinates of trapezoid ?

A ( ) ( ) ( ) ( )

B ( ) ( ) ( ) ( )

C ( ) ( ) ( ) ( )

D ( ) ( ) ( ) ( )

4 The pentagon shown is regular and has rotational symmetry. What is the angle of rotation?

A 45 C 90

B 72 D 60

5 What specific figures are formed when you draw in the six radii of this regular hexagon?

A 3 Squares C 2 Rectangles

B 6 Equilateral triangles D 6 Isosceles triangles

6 Will the rotation of a pair of parallel lines always result in another pair of parallel lines?

A Yes, they will remain parallel to each other through any rotation.

B Only if the lines are rotated 180° or 360°.

C No, they will always result in intersecting lines.

D No, they will always result in perpendicular lines.

7 Square ABCD, shown at the right, is translated up 3 units and right 2 units to produce rectangle A’B’C’D’. Which statement is true?

A ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ and ̅̅ ̅̅ ̅̅ ̅̅ ̅̅

B ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ and ̅̅ ̅̅ ̅̅ ̅̅ ̅̅

C 2 and 3

D and

8 Square ABCD, shown at the right, is translated up 3 units and right 2 units to produce rectangle A’B’C’D’. Which statement is true?

A ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ and ̅̅ ̅̅ ̅̅ ̅̅ ̅̅

B ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ and ̅̅ ̅̅ ̅̅ ̅̅ ̅̅

C 2 and 3

D and

9 Will the rotation of a pair of parallel lines always result in another pair of parallel lines?

A Yes, they will remain parallel to each

other through any rotation. C No, they will always result in

intersecting lines.

B Only if the lines are rotated 180° or 360°.

D No, they will always result in perpendicular lines.

10. What would be the image point B after a reflection over the line y = 2 and a translation 4 units right and 2 units down?

A (1, 4) C (1, -4)

B (11, -4) D (1, 0)

11 Steve created this design for a wall mural.

Which describes the translation from figure 1 to figure 2?

A up 3 units and right 1 unit

C up 4 units and right 4 units

B down 1 unit and left 3 units D down 4 units and left 4 units

y

x 0 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6

1

-5

-4 -3

-2 -1

2

3 4 5 6

-6

B

12 Which description MOST accurately describes a dilation?

A When a shape is dilated, the parallel lines remain parallel.

B When a shape is dilated, the angles within the shape change.

C When a shape is dilated, the orientation of the shape changes.

D When a shape is dilated, the distance between points remains the same.

13 Given: Quadrilateral ABCD on this graph. Which graph shows the reflection of ABCD over line l?

A

C

B

D

14 Mary Ann drew two lines on the chalkboard. Her two lines lie in the same plane but share no common points. Which could be a description of Mary Ann’s drawing?

A A set of skew lines C A set of adjacent rays

B A set of parallel lines

D A set of collinear points

15 Lines and are parallel. The , and the .

Which statement explains why you can use the equation to solve for ?

A Alternate exterior angles are congruent.

B Alternate interior angles are congruent.

C Complementary angles are congruent.

D Corresponding angles are congruent.

16 Greg used a compass and straight edge to draw the construction below.

Which of these is shown by this construction?

A The medians of a triangle are concurrent.

B The altitudes of a triangle are concurrent

C The angle bisectors of a triangle are concurrent

D The perpendicular bisectors of a triangle are congruent

17 A line segment has endpoints and . Which point divides the line segment in the ratio ?

A (-4, 3) C (0, 1)

B (-1, 4) D (1, 5.5)

18 A line is perpendicular to the line for the equation: . What is the slope of the perpendicular line?

A

C

B

D

19 Points P, Q, and R are shown below. If these points are all vertices of a parallelogram then which point would represent the coordinates of the fourth vertex of parallelogram PRQS.

A (4,6)

B (8,-1)

C (5,2)

D (9,1)

P R

Q

20 What is the coordinate of the midpoint of ?

A -2 C 3

B -1 D 6

21 What is the perimeter of the triangle shown below?

A 18

B 20

C 52

D 134

22 Square EFGH is shown below. A dilation of 2 centered at (2,2) is performed. The resulting square is labeled E’F’G’H’.

What is the length of ̅̅ ̅̅ ̅ ?

A 2 units

B 3 units

C 5 units

D 6 units

23 Which of the following is unnecessary to prove that the 2 base angles of an isosceles triangle are congruent?

A The angle sum theorem for triangles C The definition of an angle bisector

B SAS postulate D The definition of congruent triangles

24 Which of the following is necessary to prove that a triangle's exterior angle equals the sum of the two remote interior angles?

A The definition of complementary angles C The definition of supplementary angles

B The definition of an angle bisector D The definition of congruent triangles

25 A segment connects the midpoints on two sides of a triangle. What is true about this segment?

A It is always horizontal and half the length of each side

C It is always parallel to the third side and half as long as the third side

B It is always perpendicular to the two sides it joins and forms an isosceles triangle with the portions of the sides above it

D It is always half the length of those two sides and parallel to the third

26 When proving the exterior angle sum theorem, the first step is to show that an exterior angle of a polygon and an interior angle of a polygon add together to equal 180 degrees. Which angle classification justifies this step?

A Vertical angles

C Complementary angles

B Corresponding angles

D Linear pair of angles

27

𝑅 and are the midpoints of 𝑋 and 𝑌, respectively. 𝑋𝑌 𝑅

What does the midpoint theorem tell us about the

relationship between 𝑅 ̅̅̅̅ and 𝑋𝑌̅̅ ̅̅ ?

A 𝑅 ̅̅̅̅ is

the length of 𝑋𝑌̅̅ ̅̅ C 𝑅 ̅̅̅̅ and 𝑋𝑌̅̅ ̅̅ are not related by that

theorem

B 𝑅 ̅̅̅̅ is twice the length of 𝑋𝑌̅̅ ̅̅ D 𝑅 ̅̅̅̅ and 𝑋𝑌̅̅ ̅̅ are equal in length

28

Which diagram shows a triangle drawn so that it is congruent to ?

A

C

B

D

29 Triangle is rotated to become triangle . Without the use of any measurement devices, which could be used to prove that triangle is congruent to triangle ?

A SAS because both are right triangles, is congruent to , and is congruent

to

B ASA because both are right triangles and is congruent to

C SAS because both are right triangles, is congruent to , and is congruent

to

D ASA because both are right triangles, angle is congruent to angle , and is

congruent to

30 Triangle is rotated, reflected, and translated to yield triangle . Which statement proves that the two triangles are congruent?

A is taken to , and is taken to .

B is taken to , and is taken to .

C is taken to , is taken to , and is taken to .

D is taken to , is taken to , and is taken to .

31 In the diagram below, what is the measure of if the triangles and are similar?

A

B

C

D

32 Which of the triangles below is similar to ΔXYZ?

A

C

B

D All of the above

33 Which statement correctly completes the sentence below? If two distinct pairs of angles in two triangles are congruent, then _______________.

A the pair of included sides must also be congruent and the triangles must be congruent

B the pair of included sides must also be congruent and the triangles must be similar

C the third pair of angles must also be congruent and the triangles must be congruent

D the third pair of angles must also be congruent and the triangles must be similar

34 Quadrilateral ABCD is inscribed in circle Y, as shown to the right. Which property could NOT be used to find the

measure of from the information given?

A The sum of the interior angles in a triangle is

C An intercepted arc is twice the measure of the inscribed angle.

B A triangle inscribed in a semicircle is a right triangle.

D Opposite angles of inscribed quadrilaterals are supplementary

35 (review)The dotted lines in the figure below show how Jenny inscribed circle in right triangle on a practice test.

What should Jenny have done differently to answer the question correctly?

A Jenny should have used the altitudes of the triangle to find the incenter.

B Jenny should have constructed an inscribed circle. Circle is circumscribed.

C Jenny should have used the bisectors of angles , , and to find the incenter.

D Jenny should have put points , , and at the midpoints of the sides of the triangle.

2013-2014 UCS Geometry SEMESTER 1 REVIEW GUIDE #2

1. The following picture is a reflection of the image and preimage over what line?

2. What is the image of that results from a 90 clockwise rotation, using the origin as

the center of rotation?

3. Looking at the angles of the figure, what is rotational symmetry?

4. For a circus act, a trapeze artist swings along the path shown in the coordinate grid. Next, the trapeze artist swings along the same path, but 12 feet higher from the original starting point.

A

C

B

D

5. Terry made this quilt with the pattern shown. Which transformations best describe the relationship between block A and block B ?

A Two flips C A flip and a slide

B Two slides D None of the above

6. Which transformation, when performed individually, would transform the rectangle below onto itself?

A A clockwise rotation 180 about the origin

C A reflection across the x-axis, followed by a translation up 6 units

B A clockwise rotation 180 about the

point D A reflection across the y-axis, followed

by a translation left 12 units

7. The trapezoid below is rotated about point B. What is the value of x?

8. The “F” below is going to be translated 4 units down and 3 units to the right and then translated 2 units up and 1 unit to the right.

Which of the following single transformations would have the same effect on the “F” as performing both of the transformations listed above?

A Translating the “F” 2 units down and 4 units to the right

B Translating the “F” 6 units down and 2 units to the right

C Rotating the “F” 180 counterclockwise about the origin

D Reflecting the “F” over the x-axis

B

𝟑𝒚

y

x 0 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6

1

-5

-4

-3

-2

-1

2

3

4

5

6

-6

9. The point (2, 3) is reflected over the x-axis and then translated 4 units to the left and 2 units up. What are the new coordinates of the point?

10. Paul and Janelle are getting ready to play a board game. Paul sets up his pieces as shown in this diagram.

Janelle’s pieces will be set up the same way but

reflected across the line

. Which of these

coordinates represents one of Janelle’s pieces?

11. Rectangle KLMN is shown below. If KLMN undergoes a dilation of 2 centered on the origin to produce K’L’M’N’, which statement is correct?

A The equation of the line passing through points N and K is the same as the equation of the line passing through N’ and K’.

B The equation of the line passing through points M and N is the same as the equation of the line passing through M’ and N’.

C The equation of the line passing through points L and M is the same as the equation of the line passing through L’ and M’.

D The equation of the line passing through points K and L is the same as the equation of the line passing through K’ and L’.

12. Pentagon PENTA undergoes a dilation of 2.5 to produce pentagon P’E’N’T’A’. Which ratio

is equivalent to the ratio of the length of ̅̅ ̅̅ to the length of ̅̅ ̅̅ ̅̅ ?

13. Which term does NOT have a formal geometric definition?

A Angle

C Plane

B Circle

D Sphere

15. What is the first step in constructing a line segment perpendicular to line segment AB that passes through the point P as shown below?

14. Lines q and r are parallel. The measure of and the

measure of . Why can you use the equation

to solve for ?

.

•P A B

16. Construct an equilateral triangle inscribed in a circle.

17. Find the equation of the line passing through the point (–3,–4) and is parallel to the line

having the equation: .

18. Write an equation for line t can be written as

. Perpendicular to line t is line

u, which passes through the point (-2,1). What is the equation of line u?

20. In a triangle with coordinates (1, 4), (2, 8), and (5, 4), what would be the perimeter rounded to the nearest hundredth?

19. What is the midpoint of ̅̅ ̅̅ if the coordinate of A is (3, -4) and the coordinate of B is (-7, 10)?

21. How could a student determine that a triangle and its transformed image are congruent?

A They are congruent if and only if the triangles are right triangles.

B They are congruent if and only if the transformed figure was not rotated.

C They are congruent if and only if corresponding pairs of sides and corresponding

pairs of angles are congruent.

D They are congruent if and only if corresponding pairs of sides are similar and

corresponding pairs of angles are similar.

22. Which translation from solid-lined figure to dashed-lined figure is 3 units left and 3 units up? Careful, the units are by 2’s.

A

C

B

D

23.

25. In the figure below, triangle is congruent to triangle . Which transformation would maintain the congruence of the triangles? I. Reflecting triangle over II. Rotating triangle clockwise about point III. Dilating triangle by , with as the center of dilation

A I only

B III only

C I and II only

D II and III only

24. is reflected across the y-axis.

Which set of congruence statements explains why the triangles are congruent?

A and ; : SAS

B and ; : ASA

C ; ; : SSS

D ; ; : AAA

27. Two frame houses are built, a taller one next to a shorter one. If the frame houses are to be similar in their construction, what should the dimensions of the bigger house be?

28. Which steps correctly state how to construct the circumscribed circle of a triangle?

A To find the center of the circumscribed circle, find the point of concurrence of the three internal angle bisectors. The radius of the circle is the segment that joins the center and one side of the triangle and is perpendicular to the side.

B To find the center of the circumscribed circle, find the point of concurrence of the three medians of the triangle. The radius of the circle is the segment that joins the center and one of the vertices of the triangle.

C To find the center of the circumscribed circle, find the point of concurrence of the three altitudes. The radius of the circle is the segment that joins the center and one of the vertices of the triangle.

D To find the center of the circumscribed circle, find the point of concurrence of the three perpendicular bisectors. The radius of the circle is the segment that joins the center and one of the vertices of the triangle.

26. What is necessary to prove that a triangle's exterior angle equals the sum of the two remote interior angles?

30. Which steps correctly state how to construct the circumscribed circle of a triangle?

A To find the center of the circumscribed circle, find the point of concurrence of the three internal angle bisectors. The radius of the circle is the segment that joins the center and one side of the triangle and is perpendicular to the side.

B To find the center of the circumscribed circle, find the point of concurrence of the three medians of the triangle. The radius of the circle is the segment that joins the center and one of the vertices of the triangle.

C To find the center of the circumscribed circle, find the point of concurrence of the three altitudes. The radius of the circle is the segment that joins the center and one of the vertices of the triangle.

D To find the center of the circumscribed circle, find the point of concurrence of the three perpendicular bisectors. The radius of the circle is the segment that joins the center and one of the vertices of the triangle.

29. Which of the other triangles is similar to ΔABC and why?

A

C

B

D

None of the above

31. A dilation with a scale factor of 2 is applied to to produce . If measure of and the measure of what are the measures of

32. is a right triangle. CH is a perpendicular bisector that

goes from vertex C to the hypotenuse AB of the triangle. How many similar triangles are there?

33. Find the missing side lengths of BC and DC if

A

B

C

11

26

D

E

F

27.5 42.5

34.

35.

What is the measure of in the diagram above?

Quadrilateral ABCD is inscribed circle O

What is true about 𝐴 and 𝐶

135°