POWER TEST—FIRST SEMESTERGeometry K. Santos

Power Test Format (10 questions)

Angles

vertical angles—are congruent

linear pair—are supplementary

complementary angles—add to 90

supplementary angles—add to 180

perpendicular lines—form right angle

Parallel lines

corresponding angles—congruent

alternate interior angles—congruent

same-side interior angles—supplementary

Triangles

sum of the three angles is 180

exterior angles = sum of the 2 remote interior angles

Angles—vertical angles (sample #8)

Vertical angles are congruent

9x

126

9x = 126

x = 14

Angles—vertical angles (sample #4)

Vertical angles are congruent

3x – 15 2x + 13

3x – 15 = 2x + 13x – 15 = 13x = 28

Answer question asked---find the measure of an angle3(28) – 15 = 69 or 2(28) + 13 = 69

Angles—Linear Pair (sample #3)

Linear pair is supplementary (adds to 180

5x 4x - 27

5x + 4x – 27 = 180

9x – 27 = 180

9x = 207

x = 23

Answer question asked—find m<2

4(23) – 27 so m< 2 = 65

Angles—complementary angles (not on sample but shows up on power tests)

Complementary angles—add to 90

3x

57

3x + 57 = 90

3x = 33

x = 11

Angles—complementary ratio problem(sample #10)

Complementary—angles add to 90

Two complementary angles are in the ratio of 1:4.

1:4 think 1x:4x

So if complementary: 1x + 4x = 90

5x = 90

x = 18

Answer the question—find the larger angle

4x is larger than 1x

4(18) = 72

Angles—supplementary ratio problem(not on this power test)

Supplementary angles—add to 180

Two supplementary angles are in the ratio of 2:3. Find the smaller angles

2:3 think 2x:3x

Supplementary: 2x + 3x = 180

5x = 180

x = 36

Answer the question asked—find the smaller angle

2x smaller than 3x

2(36)= 72

Angles—supplement word problem(sample question #7)

One angle is 20 less than its supplement. Find the angle.

x: the angle 180 – x: its supplement

One angle is 20 less than its supplement x = (180 – x) – 20

x = 180 – x - 20 x = 160 - x

2x = 160 x = 80

Remember, x was the angle, so the angle is 80

Angles—Complement word problem(not on this sample power test)

One angle is 40 more than its complement. Find the angle.x: the angle 90 – x: its complement

x = (90 – x) + 40x = 90 – x + 40x = 130 – x2x = 130x = 65 which is the angle

So watch for complement or supplementwatch of more than or less than

Parallel Lines—corresponding angles (sample example #6)

Corresponding angles---congruent

5x - 7

2x + 41

5x – 7 = 2x + 41

3x – 7 = 41

3x = 48

x = 16

Answer the question asked—find an angle

2(16) + 41 = 73 or 5(16) – 7 = 73

Parallel Lines—Alternate interior angles (no example on this power test)

Alternate interior angles—congruent

6x - 10

4x + 18

6x – 10 = 4x + 18

2x – 10 = 18

2x = 28

x = 14

Parallel Lines—same side interior angles (example #1 on sample power test)

Same side interior angles—supplementary (add to 180

2x

7x

2x + 7x = 180

9x = 180

x = 20

Triangles—interior angle sum (example #5)

Triangle angle sum--180

6x

2x 4x

2x + 4x + 6x = 180

12x = 180

x = 15

Be careful—sometimes they ask for a particular angle

Triangles—exterior angle sum--numeric(example #2 on the sample power test)

Exterior angle = sum of the 2 remote interior angles

62

x 112

112 = x + 62

50 = x

Triangles—exterior angle sum—algebraic (example #9 on sample power test)

Exterior angle = sum of the 2 remote interior angles4x

3x 154

154 = 3x + 4x154 = 7x22 = x

Answer the question asked—measure of smaller angle (3x) 3(22) so the smaller angle measures 66