Name: ____________________________________
Teacher: Mr. Villegas
1. Parallel lines l and m are cut by transversals s and t to form the diagram below.
What is the value of x?
1. 40° 3. 120°
2. 80° 4. 140°
2. As shown in the diagram below of ∆ABC, Which statement is true?
1. 2. 3. 4. AC > AB
AB > BC
BC < AC
AC < AB
is extended through D, m∠A = 70, and m∠​ACD = 115.
3. Parallel lines l and m are cut by transversals s and t to form the diagram below.
What is the value of x?
1. 58° 3. 96°
2. 64° 4. 116°
4. In ∆ABC, m∠CAB = 2x and m∠​ACB = x + 30. If 5x − 50. What is the value of x?
1. 25 3. 40
2. 30 4. 46
is extended through point B to point D, m∠​CBD =
5. As shown in the diagram below, lines m and n are cut by transversal p.
If m∠1 = 4x + 14 and m∠2 = 8x + 10, lines m and n are parallel when x equals
1. 1 3. 13
2. 6 4. 17
6. Steve drew line segments ABCD, EFG, BF, and CF as shown in the diagram below. Scalene ∆BFC is formed.
Which statement will allow Steve to prove 1. 2. 3. 4. ∠CFG ≅ ∠FCB
∠ABF ​≅ ∠BFC
∠EFB ≅ ∠CFB
∠CBF ​≅ ∠GFC
?
7. In the diagram below, line is parallel to line m, and line w is a transversal.
If m∠2 = 3x + 17 and m∠3 = 5x - 21, what is m∠1?
1. 19 3. 74
2. 23 4. 86
Figure 1
Use the diagram below to answer the question.
8. [Refer to figure 1]
What is the measure of ∠ 2?
1. 169° 3. 129°
2. 134° 4. 113°
9. In the diagram below, || and line segment HF are drawn.
. Transversal If m∠HFG = 130 and m∠EHF = 70, what is
m∠ABE?
1. 40 3. 60
2. 50 4. 70
10. Which triangle below appears to be a right triangle?
12. In the diagram below, transversal and at V and W, respectively.
intersects 1. 2. 3. If m∠TVQ = 5x - 22 and m∠VWS = 3x + 10, for
which value of x is PQ RS?
1. 6 3. 24
2. 16 4. 28
4. 13. In the diagram below, and ΔABC are shown
with m∠A = 60° and m∠ABT = 125°.
11. Peach Street and Cherry Street are parallel. Apple
Street intersects them, as shown in the diagram below.
What is m∠ACR?
If m∠1 = 2x + 36 and m∠2 = 7x – 9, what is m∠1?
1. 9 3. 54
2. 17 4. 70
1. 125 3. 65
2. 115 4. 55
14. In the diagram of ΔABC below, is extended to point D.
If m∠CAB = x + 40, m∠ACB = 3x + 10, and m∠CBD = 6x, what is m∠CAB?
1. 13 3. 53
2. 25 4. 65
15. Transversal intersects and , as shown in the diagram below.
Which statement could always be used to prove 1. 2. 3. 4. || ?
∠2 ≅ ∠4
∠7 ≅ ∠8
∠3 and ∠6 are supplementary
∠1 and ∠5 are supplementary
16. In ΔABC, m∠A = 3x + 1, m∠B = 4x – 17, and m∠C = 5x – 20. Which type of triangle is ΔABC?
1. right 3. isosceles
2. scalene 4. equilateral
17. The diagram below shows ΔABD, with , ⊥ , and ∠EBD ≅ ∠CBD.
If m∠ABE = 52, what is m∠D?
1. 26 3. 52
2. 38 4. 64
18. In the diagram below of ΔABC ≅ , m∠A = 3x, and m∠B = x + 20.
What is the value of x?
1. 10 3. 32
2. 28 4. 40
19. In ΔJKL, 1. 61 3. 116
2. 64 4. 122
≅ . If m∠J = 58, then m∠L is
20. In the diagram of ΔJEA below, m∠JEA = 90 and mEAJ = 48. Line segment MS connects points M and S
on the triangle, such that m∠EMS = 59.
What is m∠JSM?
1. 163 3. 42
2. 121 4. 17
Figure 2
Use the information and the diagram below to answer the following question.
Lines w and z are cut by transversals l and m.
21. [Refer to figure 2]
What is the measure of ∠ 2 that makes lines w and z
parallel?
1. 148° 3. 68°
2. 132° 4. 32°
22. In the diagram below, ΔLMO is isosceles with LO =
MO.
If m∠L = 55 and m∠NOM = 28, what is m∠N?
1. 27 3. 42
2. 28 4. 70
23. The accompanying diagram shows the construction of line . Which principle is used in the proof for this construction?
through given point P and parallel to given line 1. If two lines are parallel, then the alternate exterior angles are congruent.
2. If two lines are cut by a transversal so that a pair of alternate interior angles are congruent, then the lines are
parallel.
3. If two lines are cut by a transversal so that the interior angles on the same side of the transversal are
supplementary, then the lines are parallel.
4. If two lines are parallel, then the corresponding angles are congruent.
24. In the accompanying diagram, m∠ ECB.
, || , || , m ∠ DAE = 34 and m ∠ DFE = 57. Find
Answer: m∠ ECB = 25. How many different triangles can be constructed with angles that measure 120°, 40°, and 60°?
1. No triangles
2. One triangle
3. More than one triangle