Write a paragraph proof. 14. Given: m∠PRQ = 90, m∠RPT = 90

17. BD ANSWER: 9
Chapter 4
Write a paragraph proof. 18. m∠BCD ANSWER: 40
19. Identify the type of congruence transformation show
reflection, translation, or rotation.
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
by the Reflexive
∠PRQ
∠RPT.
Property. Therefore, QRP TPR by AAS.
15. What is the approximate width of the creek shown
below? Explain your reasoning.
ANSWER: 57 ft; Since ∠T and ∠R are both right angles, ∠T
∠R. Because they are vertical angles, ∠TSU
∠RSQ. TS = RS = 60,
so
. Therefore,
by
ASA. That means that QR = TU = 57 ft.
Find each measure. 16. m∠BDA ANSWER: 60
17. BD ANSWER: rotation
Graph each pair of triangles with the given
vertices. Then, identify the transformation, and
verify that it is a congruence transformation.
21. A(–1, –1), B(–1, –4), C(2, –4); M (–1, 1), N(–4, 1), P
(–4, 4)
ANSWER: 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.
ANSWER: 9
18. m∠BCD eSolutions
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ANSWER: 40
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