Classify each triangle as acute, equiangular, obtuse, or right, and as

Chapter 4
Classify each triangle as acute, equiangular, obtuse, or right, and as equilateral, isosceles, or scalene.
2. BCD
ANSWER: right; isosceles
4. In the bicycle shown, m∠C = 60 and m∠D = 105. Find m∠B.
ANSWER: 45
Find each measure.
6. m∠2 ANSWER: 75
In the figure,
. Find each value.
8. x
ANSWER: 5
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ANSWER: Page 1
8. x
ANSWER: Chapter 4
5
10. z ANSWER: 11
Determine whether PQR XYZ. Explain. 12. P(–2, 4), Q(–7, 3), R(0, 9); X(3, 6), Y(2, 1), Z(8, 8)
ANSWER: PQ =
, QR =
, PQ =
, XY =
same measure, so the triangles are congruent.
, YZ =
PQR
, XZ =
. Each pair of corresponding sides has the
XYZ by SSS.
Write a paragraph proof. 14. Given: m∠PRQ = 90, m∠RPT = 90, ∠Q
Prove: QRP TPR
∠T
ANSWER: We are given that ∠Q
∠T, m∠PRQ = 90, and m∠RPT = 90. Using the Substitution Property and the definition
of congruence, we can determine that ∠PRQ
by the Reflexive Property. Therefore, QRP
∠RPT.
TPR by AAS.
Find each measure. 16. m∠BDA ANSWER: 60
18. m∠BCD ANSWER: 40
Graph each pair of triangles with the given vertices. Then, identify the transformation, and verify that it is
a congruence transformation.
20. A(2, 2), B(4, –1), C(1, –2); M (–4, –1), N(–1, –2), P(–2, 2)
ANSWER: reflection;
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18. m∠BCD ANSWER: Chapter
4
40
Graph each pair of triangles with the given vertices. Then, identify the transformation, and verify that it is
a congruence transformation.
20. A(2, 2), B(4, –1), C(1, –2); M (–4, –1), N(–1, –2), P(–2, 2)
ANSWER: reflection;
22. The gym at Alex’s school is located 70 feet south and 90 feet west of the main building. The vocational building is
located 120 feet south and 200 feet east of the main building. Show that the triangle formed by these three buildings
is scalene. Explain your reasoning.
ANSWER: Let the coordinates (0,0) represent the location of the main building, (–90, –70) represent the location of the gym, and
(200, –120) represent the location of the vocational building. The distance from the main building to the gym is or about 114 feet. The distance from the gym to the vocational building is or about 233 feet. The distance from the gym to the vocational building is or about 294 feet. Since none of these distances are the same, the
triangle formed by these three buildings is scalene.
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