Power Test*first Semester

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POWER TEST—FIRST
SEMESTER
Geometry
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 + 13
x – 15 = 13
x = 28
Answer question asked---find the measure of an angle
3(28) – 15 = 69°
or
2(28) + 13 = 69°
Angles—Linear Pair (sample #3)
Linear pair is supplementary (adds to 180°)
5x
5x + 4x – 27 = 180
9x – 27 = 180
9x = 207
x = 23
Answer question asked—find m<2
4(23) – 27
so m< 2 = 65°
4x - 27
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) + 40
x = 90 – x + 40
x = 130 – x
2x = 130
x = 65° which is the angle
So watch for complement or supplement
watch 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 = x + 62
50° = x
112
Triangles—exterior angle sum—algebraic
(example #9 on sample power test)
Exterior angle = sum of the 2 remote interior angles
4x
3x
154
154 = 3x + 4x
154 = 7x
22 = x
Answer the question asked—measure of smaller angle (3x)
3(22) so the smaller angle measures 66°

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