Review for Exam on Triangles
1.
Page 1 of 6
3.
If the hypotenuse of a right triangle is 6 and one leg
is 5, the other leg is
1.
2. 61
3.
4. 11
2.
If the length of a rectangle is 3 and the width is 2, the
length of the diagonal is:
1.
2.
3. 5
4. 13
Figure 1
A 10-foot ladder is placed against the side of a
building, as shown in Figure 1. The bottom of the
ladder is 8 feet from the base of the building. In order
to increase the reach of the ladder against the
building, it is moved 4 feet closer to the base of the
building, as shown in Figure 2. To the nearest foot,
how much further up the building does the ladder
now reach?
1. 1 foot
2. 3 feet
3. 6 feet
4. 9 feet
4.
Figure 2
In the diagram of ΔABC, m∠ACB = 90 and
an altitude. If AD = 2 and DB = 6, find AC.
is
1.
2. 4
3. 6
4. 4
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Review for Exam on Triangles
5.
Page 2 of 6
8.
Which set of numbers could not represent the lengths
of the sides of a right triangle?
1.
2.
3.
4.
{3, 4, 5}
{6, 9, 12}
{5, 12, 13}
{8, 15, 17}
6.
In right triangle ABC,
is the altitude drawn to
hypotenuse
. If AD = 6 and DB = 24, find CD.
1.
2.
3.
4.
12
12
6
144
7.
Figure 3
In the diagram:
,
∠E, and C is the midpoint of
justifies ΔABC ≅ ΔEDC ?
1. SSS ≅ SSS
2. SAS ≅ SAS
, and
, ∠A ≅
. Which theorem
3. ASA ≅ ASA
4. SSA ≅ SSA
9.
Find the length of a leg of an isosceles right triangle
whose hypotenuse measures 8
.
1.
2.
3.
4.
8
4
8
16
Figure 4
In the diagram:
,
, and M is the
midpoint of
. Which statement could be used to
prove ΔTMR ≅ ΔPML?
1. SAS ≅ SAS
2. AAS ≅ AAS
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3. HL ≅ HL
4. SSS ≅ SSS
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Review for Exam on Triangles
Page 3 of 6
10.
13.
Figure 5
Figure 6
In the diagram of right triangle ABC:
is an
altitude drawn to hypotenuse
, AC = 20, AD <
DC, and BD = 6.
(a) AD =
, and DC =
.
(b) To the nearest tenth of a unit, AB =
.
In the diagram of quadrilateral ABCD,
is a
diagonal that bisects ∠BAD and ∠BCD. Which
statement can be used to prove that ΔABC ≅ ΔADC?
1. HL ≅ HL
2. SSS ≅ SSS
3. ASA ≅ ASA
4. SAS ≅ SAS
14.
11.
If the altitude is drawn to the hypotenuse of a right
triangle, then the two triangles formed are always
1.
2.
3.
4.
congruent
equal in area
isosceles
similar
Figure 7
12.
What is the length of the altitude of an equilateral
triangle whose side has length 4?
1.
2.
3.
4.
2
2
4
4
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In the diagram,
≅
,
⊥
, and
⊥
. Which statement can be used to prove that
ΔPQR ≅ ΔSRQ?
1. AAS ≅ AAS
2. SAS ≅ SAS
3. HL ≅ HL
4. SSS ≅ SSS
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Review for Exam on Triangles
Page 4 of 6
15.
18.
The set of integers {3,4,5} is a Pythagorean triple.
Another such set is
Three sides of a triangle measure 4, 5, and 8. Find the
length of the longest side of a similar triangle whose
perimeter is 51.
1. {6, 7, 8}
2. {6, 8, 12}
3. {6, 12, 13}
4. {8, 15, 17}
1. 3
2. 12
3. 15
4. 24
16.
19.
Which condition does not prove that two triangles
are congruent?
1. SSS ≅ SSS
2. SSA ≅ SSA
3. SAS ≅ SAS
4. ASA ≅ ASA
17.
The accompanying diagram shows a 24-foot ladder
Figure 8
leaning against a building. A steel brace extends
from the ladder to the point where the building meets
the ground. The brace forms a right angle with the
In the diagram of ABC:
ladder.
and DE = 9. Find AC.
1. 9
2. 6
||
, DB = 6, AD = 2,
3. 3
4. 12
20.
Find the length of the line segment that joins the
midpoints of two sides of a triangle whose third side
is 10.
If the steel brace is connected to the ladder at a point
1. 5
that is 10 feet from the foot of the ladder, which
equation can be used to find the length, x, of the steel 2. 7
brace?
3. 10
4. 12
1.
2.
3. 102 + x2 = 142
4. 102 + x2 = 242
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Review for Exam on Triangles
Page 5 of 6
23.
21.
Figure 11
Figure 9
In the diagram of ABC,
and AE = 5. Find EC.
In the diagram of CAT, W is a point on
and G
is a point on
such that
is parallel to
, TG =
1. 5
x, GC = x 1, CW = x + 5, and WA = 2x + 6.
2. 10
TG =
24.
||
, AD = 3, AB = 9,
3. 12
4. 15
22.
Figure 12
In the figure,
and
are parallel, AD = 10, AB
= 24, and AC = 36. Find AE.
Figure 10
In the diagram of ABC:
,
,
,
, BF = 8, FA = 12, FE = 9, and BC = x.
What is the value of x?
1. 3
2. 5.4
3. 6
4. 15
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1. 11
2. 12
3. 14
4. 15
25.
Which statement about two equilateral triangles is
always true?
1.
2.
3.
4.
They are similar.
They are congruent.
They are equal in area.
They have congruent altitudes.
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Review for Exam on Triangles
26.
Page 6 of 6
28.
Delroy's sailboat has two sails that are similar
triangles. The larger sail has sides of 10 feet, 24 feet,
and 26 feet. If the shortest side of the smaller sail
measures 6 feet, what is the perimeter of the smaller
sail?
Figure 13
1. 15 ft
2. 36 ft
3. 60 ft
4. 100 ft
In the diagram of ABC,
||
,
, CD
= 6, DA = 4, and CF = 5. What is the length of
? 29.
1. 1
2. 3
3. 5
4. 10
27.
The accompanying diagram shows two similar
triangles.
How many integers values of x are there so that x, 5,
and 8 could be the lengths of the sides of a triangle?
1. 6
2. 9
3. 3
4. 13
30.
If two sides of a triangle have lengths 4 and 9, then
the length of the third side may be any number
1.
2.
3.
4.
greater than 4 but less than 9
greater than 5
less than 13
greater than 5 but less than 13
Which proportion could be used to solve for x?
1.
2.
3.
4.
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