In ARST, the altitudes of the triangle intersect at a point in the interior of the triangle. The lengths of the sides of ARST are RS = 14, ST = 15, and TR = 13. а) If TX 12, find RX and XS. (HINT: Use the Pythagorean Theorem.) b) If RY 168 find TY and YS. 15 c) If SZ 168 find ZR and TZ. 13 > d) Use results from parts (a), (b), and (c) to show that RX SY TZ XS YT ZR 1. Y R S
In ARST, the altitudes of the triangle intersect at a point in the interior of the triangle. The lengths of the sides of ARST are RS = 14, ST = 15, and TR = 13. а) If TX 12, find RX and XS. (HINT: Use the Pythagorean Theorem.) b) If RY 168 find TY and YS. 15 c) If SZ 168 find ZR and TZ. 13 > d) Use results from parts (a), (b), and (c) to show that RX SY TZ XS YT ZR 1. Y R S
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter3: Triangles
Section3.4: Basic Constructions Justified
Problem 38E
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Question
![In ARST, the altitudes of the triangle intersect at a point
in the interior of the triangle. The lengths of the sides of
ARST are RS = 14, ST = 15, and TR = 13.
а) If TX
12, find RX and XS.
(HINT: Use the Pythagorean Theorem.)
b) If RY
168
find TY and YS.
15
c) If SZ
168
find ZR and TZ.
13 >
d) Use results from parts (a), (b), and (c) to show that
RX SY TZ
XS YT ZR
1.
Y
R
S](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2dc2436c-40d2-4cb9-bef0-e9f1f7252406%2Fc34df699-89dc-48a3-a361-828c02ab80ae%2Fsw6xqr9_processed.png&w=3840&q=75)
Transcribed Image Text:In ARST, the altitudes of the triangle intersect at a point
in the interior of the triangle. The lengths of the sides of
ARST are RS = 14, ST = 15, and TR = 13.
а) If TX
12, find RX and XS.
(HINT: Use the Pythagorean Theorem.)
b) If RY
168
find TY and YS.
15
c) If SZ
168
find ZR and TZ.
13 >
d) Use results from parts (a), (b), and (c) to show that
RX SY TZ
XS YT ZR
1.
Y
R
S
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