11/12/13
POW #7 - Geo 2013
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Teacher: Ms. Williams
1.
4.
Which best completes the sentence?
If triangles 1 and 2 are congruent, then a congruence statement
could be ΔCAB ≅ ________.
1. ΔDEF
3. ΔEFD
2. ΔFED
4. ΔFDE
Figure 1
-------------2.
In the diagram, ∠ ACD is an exterior angle of ΔABC. If m∠ B =
40, m∠ A = 2x, and m∠ ACD = 3x, what is the value of x?
The measures of the three angles of a triangle are represented
by x, 3x, and x + 30. Find the value of x.
1. 40
3. 8
2. 28
4. 20
1. 15
3. 42
2. 30
4. 65
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5.
If the angles of a triangle are represented by x, 3x + 20, and 6x,
the triangle must be
3.
In the diagram of ΔABC,
, and m∠ A = 70.
1. obtuse
3. acute
2. right
4. isoceles
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6.
What is the measure of the largest angle of a triangle whose
angles measures are in the ratio of 2:3:4?
Find the measure of the vertex angle.
1. 30
3. 70
2. 40
4. 110
1. 20°
3. 60°
2. 40°
4. 80°
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11/12/13
POW #7 - Geo 2013
7.
11.
The measure of the vertex angle of an isosceles triangle is three Tina wants to sew a piece of fabric into a scarf in the shape of
times the measure of a base angle. Find the number of degrees an isosceles triangle, as shown in the accompanying diagram.
in the measure of a base angle.
1. 18
3. 36
2. 24
4. 48
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8.
In triangles ABC and DEF, m∠ C = m∠ F, AC = DF, and BC =
EF. If AB = 2x − 1, BC = 2x + 5, and DE = 5x − 4, find the value
of x.
1. 1
3. 3
2. -1
4. 5
What are the values of x and y?
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1.
2.
3.
4.
9.
In ΔABC, m∠ A = 41 and m∠ B = 48. What kind of triangle is
ΔABC?
1. right
3. isosceles
2. obtuse
4. acute
-------------12.
Which condition does not prove that two triangles are
congruent?
-------------10.
Triangle ABC, with side
accompanying diagram.
x = 42 and y = 96
x = 69 and y = 69
x = 90 and y = 48
x = 96 and y = 42
extended to D, is shown in the
If m∠ ABC = 63 and m∠ BCD = 92, then m∠ BAC =
1. SSS ≅ SSS
3. SAS ≅ SAS
2. SSA ≅ SSA
4. ASA ≅ ASA
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11/12/13
POW #7 - Geo 2013
13.
15.
In the accompanying diagram of triangles BAT and FLU, ∠ B
≅ ∠ F and
≅
.
In the diagram below of ΔACD, B is a point on
such that
ΔADB is an equilateral triangle, and ΔDBC is an isosceles
triangle with
≅
. Find m∠ C.
Which statement is needed to prove ΔBAT ≅ ΔFLU?
1. ∠ A ≅ ∠ L
2.
≅
3. ∠ A ≅ ∠ U
4.
||
Answer: m∠ C =
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14.
16.
In the diagram below, ΔABC is shown with
through point D.
extended
If m∠ BCD = 6x + 2, m∠ BAC = 3x + 15, and m∠ ABC = 2x −
1, what is the value of x?
1. 12
2. 14
In the accompanying diagram,
40. What is m∠ ACD?
1. 80
3. 110
2. 70
4. 40
,
≅
, and m∠ A =
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3. 16
4. 18
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11/12/13
POW #7 - Geo 2013
17.
19.
In the diagram below, ΔABC ≅ ΔXYZ.
If the vertex angle of an isosceles triangle measures 40°, find
the number of degrees in the measure of an exterior angle at
the base of the triangle.
Answer: Exterior angle =
-------------20.
Which statement must be true?
1. ∠ C ≅ ∠ Y
2. ∠ A ≅ ∠ X
3.
4.
≅
≅
In triangle ZOE,
is extended through point E to point F.
The measure of the exterior angle E is represented by 8x – 45,
angle O is represented by 3x, and angle Z is 2x – 15. Find the
measure of angle OEZ.
Answer: m∠ OEZ =
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18.
In the diagram below of ΔGJK, H is a point on
,
≅
, m∠G = 28, and m∠ GJK = 70. Determine whether ΔGHK is an
isosceles triangle and justify your answer.
1. Yes, because angles GKH and KGH are congruent.
2. No, because angles GKH and KHJ are not congruent.
3. Yes, because there are two congruent angles in triangle
GHK.
4. No, because there are no two congruent angles in
triangle GHK.
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