1. Quarterly 3
Review

2. 2. Find the value of x: 2𝑥 + 5 5 = 𝑥 + 10 4 .
The ratio of two supplementary angles is 4:5. Find the measure of the smaller angle.
2. Find the value of x: 2𝑥 = 𝑥
smaller angle = 4x
4x + 5x = 180
smaller angle = 4 (20)
9x = 180
smaller angle = 80°
x = 20
4(2x + 5) = 5(x + 10)
8x + 20 = 5x +50
3x = 30
x = 10

3. For #3-5, use the diagram below.
trapezoid ABCD is similar to trapezoid EHGF.
3. Find x.
4. Find y.
𝑥 21 = 2 3
3𝑥=42
x = 14
10 𝑦 = 2 3
y = 15
2𝑦=30
𝐴𝐵 𝐸𝐻 = 𝐵𝐶 𝐻𝐺 = 𝐶𝐷 𝐺𝐹 = 𝐴𝐷 𝐸𝐹
𝑥 21 = 𝐵𝐶 𝐻𝐺 = = 10 𝑦
Scale Factor = = 2 3

4. For #3-5, use the diagram below.
trapezoid ABCD is similar to trapezoid EHGF.
3. Find x.
4. Find y.
5. Find m∠A.
x = 14
m∠𝐸=143°
y = 15
𝑚∠𝐴=𝑚∠𝐸
𝑚∠𝐵=𝑚∠𝐻
𝑚∠𝐶=𝑚∠𝐺
𝑚∠𝐷=𝑚∠𝐹
m∠𝐴=143° ≫ ≫

5. For #6 and #7, use the diagram below. 𝐴𝐼 ∥ 𝐷𝑆 6. Find x. 7. Find y.
𝐴𝐼 ∥ 𝐷𝑆
6. Find x.
7. Find y.
𝑦 12 = = 3 𝑥+3
3 𝑥 + 3 = 5 13
𝑥= = 4 4 5
39=5(𝑥+3)
𝑦 12 = 5 13
𝑦= =
13𝑦=60

6. 8. In isosceles ∆XYZ, 𝑋𝑌 ≅ 𝑌𝑍 . m∠Y = 40°, find m∠X and m∠Z.
x + x + 40 = 180 Y
2x + 40 = 180
40°
2x = 140
x = 70
m∠X = 70° x° x°
m∠Z = 70° X Z

7. 9. ∆MON is similar to ∆QOP. Find the scale factor.
𝑀𝑂 𝑄𝑂 = 𝑂𝑁 𝑂𝑃 = 𝑀𝑁 𝑄𝑃
9 12 = = 𝑀𝑁 𝑄𝑃
9 12 = 3 4
= 3 4
Scale Factor is 3 4

8. 10. Given: a ∥ b ∥ c
Find x.
= 21 𝑥
12x = 336
x = 28

9. AA similarity postulate
11. Are the triangles shown similar? If so, which postulate or theorem justifies the similarity.
AA similarity postulate

10. For #12 and #13, WXYZ is a parallogram.
2y + 10 = 4y – 12
22 = 2y
11 = y
32°
148°
y = 11
10x – 2 = 148
2y + 10 15
10x = 150
2(11) + 10
x = 15 11 32

11. 14. In ∆XYZ, P and Q are midpoints of 𝑋𝑌 and 𝑋𝑍
14. In ∆XYZ, P and Q are midpoints of 𝑋𝑌 and 𝑋𝑍 . PQ = (5x + 2) and YZ = (3x + 18). Find PQ.
3x + 18 = 2(5x + 2)
3x + 18 = 10x + 4
18 = 7x + 4
7x = 14
x = 2
5x + 2
PQ = 5x + 2
PQ = 5(2) + 2
3x + 18
PQ =
PQ = 12

12. 15. ABCD is a trapezoid. 𝐸𝐹 is the median
15. ABCD is a trapezoid. 𝐸𝐹 is the median AB = (x – 3), EF = 10, and DC = (2x – 4). Find x.
(x – 3) + (2x – 4) = 2(10)
3x – 7 = 20
3x = 27
x = 9
x – 3 10
2x – 4

13. 16. The given figure is a parallelogram with its diagonals drawn, find the values of x and y.
2x + 6 = 26
4y – 10 = 6
2x = 20
4y = 16
x = 10
y = 4

14. 17. Find x.
9x = 3x + 54
6x = 54
x = 9

15. 18. A regular polygon has 18 sides
18. A regular polygon has 18 sides. Find the measure of each interior angle.
𝑛−2 180 𝑛
18−
160°

16. TRUE ; 8 + 8 > 15 TRUE TRUE For #19-21, answer TRUE or FALSE.
19. A triangle may have the sides measuring 8, 8, 15.
20. The diagonals of a rectangle are congruent.
21. All equilateral triangles are similar polygons.
TRUE ; > 15
TRUE
TRUE

17. 22. If AM > AN, then m∠M ____ m∠N.
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22. If AM > AN, then m∠M ____ m∠N. 5 4

18. 23. L is the midpoint of 𝑀𝑁. ML = (2x + 3) and MN = (7x – 12). Find MN
23. L is the midpoint of 𝑀𝑁 . ML = (2x + 3) and MN = (7x – 12). Find MN. (Draw your own picture.)
2x + 3 ● M L N
7x – 12
2(2x + 3) = 7x – 12
MN = (7x – 12)
MN = 7(6) – 12
4x + 6 = 7x – 12
MN = 42 – 12
18 = 3x
MN = 30
6 = x
x = 6

19. rotation translation reflection dilation
24. Draw an example of all the transformations for the figure below.
rotation
translation
reflection
dilation

20. For #25-27, use the diagram below. 25
For #25-27, use the diagram below. 25. Name a pair of alternate interior angles, a pair of same-side interior angles, and a pair of corresponding angles.
alternate interior ∠’s:
∠3 and ∠5
same-side interior ∠ ′ s:
∠3 and ∠4
corresponding ∠’s:
∠2 and ∠5

21. 26. Solve for x: m∠3 = (7x – 10)° and m∠4 = (15x – 8)°. 27
26. Solve for x: m∠3 = (7x – 10)° and m∠4 = (15x – 8)°. 27. Solve for y: m∠2 = ( 3(y – 4) )° and m∠5 = (y + 14)°.
(7x – 10) + (15x – 8) = 180
22x – 18 = 180
22x = 198
x = 9
3(y – 4) = y + 14
3y – 12 = y + 14
2y = 26
y = 13

22. 28. What type of transformation is shown below?
rotation

23. 29. Write the definitions and draw a diagram of: Midpoint of a segment, Segment bisector, Median of a triangle, and Angle bisector.
Midpoint of a segment –
The point that divides the segment into two congruent segments.
Segment bisector –
A line, segment, ray, or plane that intersects the segment at its midpoint.

24. Median of a triangle –
A segment from a vertex to the midpoint of the opposite side.
Angle bisector –
The ray that divides the angle into two congruent adjacent angles.

25. 30. Given: 𝐴𝐶 ⊥ 𝐵𝐹 ; 𝐵𝐸 ≅ 𝐸𝐹 ; BAD  FAD Which of the following is the altitude, median, angle bisector of ∆ABF?
altitude – 𝐴𝐶
median – 𝐴𝐸
angle bisector – 𝐴𝐷

26. 31. Given: c ⊥ d. If m∠1 = (3x – 20)° and m∠2 = (5x + 6)°, find x.
(3x – 20) + (5x + 6) = 90
8x – 14 = 90
8x = 104
x = 13

27. 32. Write a two-column proof
32. Write a two-column proof. Given: 𝐸𝐷 ≅ 𝐷𝐺 ; F is the midpoint 𝐸𝐺 Prove: ∠EDF ≅ ∠GDF Statements Reasons
1. 𝐸𝐷 ≅ 𝐷𝐺
1. Given
2. F is the midpoint of 𝐸𝐺
2. Given
3. 𝐸𝐹 ≅ 𝐹𝐺
3. Definition of midpoint
4. Reflexive property
4. 𝐷𝐹 ≅ 𝐷𝐹
5. SSS Post.
5. ∆EDF ≅ ∆GDF
6. CPCTC
6. ∠EDF ≅ ∠GDF