Name __________________
Date __________________
CC Geometry H
Hwk. #21
1. ΔRST has altitude SU drawn to hypotenuse RT, ST = 15, RS = 36, RT = 39.
SUT
RUS
(1) Complete the similarity statement: ΔRST ~ Δ______
~ Δ______
(2) Complete the table of ratios.
shorter leg : hypotenuse longer leg : hypotenuse shorter leg : longer leg
ΔRST
15:39
36:39
15:36
ΔRUS
SU:36
RU:36
SU:RU
ΔSTU
TU:15
SU:15
TU:SU
(3) Use the values of the ratios to find SU.
SU = 180/13 or 13 11/13
2. Use similar triangles to find the length of altitude z.
I
25
K 4 J
z
z = 10
L
OVER
3. Given right triangle RST with altitude RU to its hypotenuse,
, and
, find the lengths of the sides of ΔRST.
RT = 7, ST = 25, RS = 24
4. Given right triangle ABC with altitude CD, find AD, BD, AB, and DC.
C
2√5
A
AD = 4, BD = 1, AB = 5, DC = 2
√5
D
B
5. In right triangle ABD, AB = 53, and altitude DC = 14. Find the lengths of BC
and AC.
BC = 4, AC = 49
or
BC = 49, AC = 4