College Prep Geometry

MID-TERM STUDY GUIDE

Mrs. Miller

Name: __________________

Due: Thursday, January 9, 2014

To receive full credit you must have

• Tried EVERY PROBLEM

• Work shown for EVERY PROBLEM

• All work done in this packet

Name: ________________________ Class: ___________________ Date: __________ ID: A

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2013-2014 CP Geometry Midterm Exam Study Guide

Short Answer

Refer to Figure 1.

Figure 1

1. Name the intersection of lines m and n.

2. Name a line that contains point G.

3. Name the plane containing lines p and m.

4. What is another name for line p?

Name: ________________________ ID: A

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5. Name three points that are collinear.

Refer to Figure 2.

Figure 2

6. How many planes are shown in the figure?

7. Name the intersection of plane DAB and a plane EBC.

Name: ________________________ ID: A

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Refer to the figure below.

8. Name all segments parallel to AB.

9. Name all segments skew to GH .

Find the measurement of the segment.

10. PR = 16.3 mm, RS = 11.2 mm

PS = ?

Use the number line to find the measure.

11. RH

Name: ________________________ ID: A

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Use the Distance Formula to find the distance between each pair of points.

12.

Find the coordinates of the midpoint of a segment having the given endpoints.

13. Q 11, 8ÊËÁÁ

ˆ¯̃̃ , R 2, 11Ê

ËÁÁˆ¯̃̃

In the figure, GK→

bisects ∠FGH .

14. If m∠FGK = 6v − 3 and m∠KGH = 3v + 6, find angle x.

Name: ________________________ ID: A

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15. The measures of two complementary angles are 8q − 5 and 8q + 15. Find the measures of the angles.

Make a conjecture about the next item in the sequence.

16. 1, − 8, − 17, − 26, − 35

17. In the figure, m∠NML = 135, PQ→←

Ä TU→←

and KL→←

Ä NM→←

. Find the measure of angle TLR.

18. In the figure, AB Ä CD. Find x and y.

Name: ________________________ ID: A

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Write the statement in if-then form.

19. Two angles measuring180 are supplementary.

20. Identify the hypothesis of the statement Two angles are complementary if they have a sum of 90 degrees..

21. Identify the conclusion of the statement Two angles are complementary if they have a sum of 90 degrees..

Determine whether the conjecture is true or false. Give a counterexample for any false conjecture.

22. Given: m2

+ 6 = 15

Conjecture: m = 3

23. Given: Two angles are adjacent.

Conjecture: They are both acute angles.

Name: ________________________ ID: A

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Use the figure to find the angles.

24. Name two acute vertical angles and two obtuse vertical angles.

Obtuse: Acute:

Explain the difference between the two answers.

25. Name a linear pair.

Name: ________________________ ID: A

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Given the following information, determine which lines are parallel. State the postulate or theorem that

justifies your answer. (Correspondong, Alternate interior/exterior, Consecutive interior/exterior, Vertical,

Linear Pair)

26. ∠2 ≅ ∠6

27. In the figure, p Ä q. Find m∠1.

Name: ________________________ ID: A

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Write an equation in point-slope form of the line having the given slope that contains the given point.

28. m = −3, −2, 1ÊËÁÁ

ˆ¯̃̃

Find each measure.

29. m∠1, m∠2, m∠3

30. m∠1, m∠2, m∠3

Name: ________________________ ID: A

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Identify the congruent triangles in the figure.

31.

Name the congruent angles and sides for the pair of congruent triangles.

32. ∆GHK ≅ ∆XZT

33. Triangle FJH is an equilateral triangle. Find x and y.

Name: ________________________ ID: A

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Refer to the figure. ∆ARM, ∆MAX, and ∆XFM are all isosceles triangles.

34. What is m∠MAX ?

35. What is m∠ARM ?

36. Which segment is the shortest possible distance from point D to plane P?

Name: ________________________ ID: A

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37. Determine the relationship (<,>,=) between ∠CPV and ∠CTK

38. Name the shortest and longest side of ABC.

Determine whether the given measures can be the lengths of the sides of a triangle. Write yes or no.

Explain.

39. 4, 6, 17

Name: ________________________ ID: A

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Refer to the figure to determine which is a true statement for the given information.

40. KN is an altitude.

41. KN is a median.

42. NK is an angle bisector.

Name: ________________________ ID: A

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43. AC is a perpendicular bisector and ∠B = 49°. Find the value of x, y, and the measure of ∠CAB. Put

your final answer on the appropriate line.

x = __________________

y = __________________

m∠CAB = _____________

Name: ________________________ ID: A

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44. Write a two-column proof for the problem. 6 steps

Given: AB ≅ ED

C is the midpoint of BD

∠B and ∠D are right angles

Prove: ABC ≅ EDC

A

B C D

E

Statements Reasons

Properties of Circles

x°

n°Tangent-Chord

x = n12

a

cx°

d

b

m° n°

2 Chords

a · b = c · d

x = (m + n)12

a

c

x°b

m°n°

Tangent-Secant

a2 = b (b + c)

x = (m − n)12

a

x°

b

m° n°

2 Tangents

a = b

x = (m − n)12

Inscribed Angle

x = n12

x°n°

2 Secants

b (a + b) = d (c + d )

x = (m − n)12

a

cx°

d

bm° n°

Angle measure is represented by x. Arc measure is represented by m and n. Lengths are given by a, b, c, and d.

Right Triangle Formulas

a

b

c

Trigonometric Ratios:

opposite

adjacent

hypotenuse

θ

opposite

hypotenusesin θ =

adjacent

hypotenusecos θ =

opposite

adjacenttan θ =

Pythagorean Theorem:

a 2 + b

2 = c 2

If a right triangle has legs withmeasures a and b and hypotenusewith measure c, then...

Coordinate Geometry Properties

Distance Formula: d = (x2 – x 1)2 + (y2 – y 1)2

Midpoint: ,

Slope: m =

Point-Slope Formula: (y − y 1) = m (x − x 1)

Slope Intercept Formula: y = mx + b

Standard Equation of a Line: Ax + By = C

y 1 + y 2

2

x 1 + x 2

2

y 2 − y 1x 2 − x 1

Formulas that you may need to solve questions on this exam are found below.

You may use calculator π or the number 3.14.

RefEFERENCEKEYSTONE

GEOMETRY FORMULA SHEET ─ PAGE 1

Copyright © 2011 by the Pennsylvania Department of Education. The materials contained in this publication may be duplicated by Pennsylvania educators for local classroom use. This permission does not extend to the duplication of materials for commercial use.

Plane Figure Formulas

c

b

h dP = b + c + d

A = bh12

Sum of angle measures = 180(n – 2), where n = number of sides

rC = 2�r A = �r 2

wP = 2l + 2wA = lw

l

s

s P = 4sA = s · s

b

ha P = 2a + 2bA = bh

a

h

b

A = h (a + b)12

P = a + b + c + dc d

Solid Figure Formulas

Euler’s Formula for Polyhedra:

V − E + F = 2

vertices minus edges plus faces = 2

r

h SA = 2�r 2 + 2�rh

V = �r 2h

SA = 2lw + 2lh + 2whV = lwh

w

h

l

r

SA = 4�r 2

V = �r 343

h

r

SA = �r 2 + �r r 2 + h 2

V = �r 2h13

SA = (Area of the base) + (number of sides)(b)( )

V = (Area of the base)(h)13

12h

base

b

b

Formulas that you may need to solve questions on this exam are found below.

You may use calculator π or the number 3.14.

RefEFERENCEKEYSTONE

Copyright © 2011 by the Pennsylvania Department of Education. The materials contained in this publication may be duplicated by Pennsylvania educators for local classroom use. This permission does not extend to the duplication of materials for commercial use.

GEOMETRY FORMULA SHEET ─ PAGE 2