CC Geometry H
Aim #19: How do we find missing segments of a right triangle with an altitiude
drawn to the hypotenuse?
Do Now: Use the diagram to complete each statement.
1. ΔCAG ~ ______
7
3 G
A
5. m≮ECD = ______
B
530
2. ΔDCF ~ ______
6. CF = _____
3. ΔACB ~ ______
7. BC = _____
4. m≮ECF = ______
8. DE = _____
450
C
D
9
F
#1-6 Find the values of the variables in each right triangle.
2.
1.
20
y
21
6
x
z
x
6.4
y
3.6
29
4.
3.
y
z
9.6
7.2
x
3
z
y
5
x
E
1
5.
2
x
6.
y
x
z
x = 4
7. If DC = 9 and DB = 15, find AD.
AD = 25
9. If AC = 9 and BC = 6, find CD.
CD = 4
8. If AD = 6 and DB = 24, find CD.
CD = 12
10. If BC = 10 and AC = 25, find AD.
AD = 21
11.Four streets in a town are illustrated in the accompanying diagram.
If the distance on Poplar Street from F to P is 12 miles and the distance on
Maple Street from E to M is 10 miles, find the distance on Maple Street, in
miles, from M to P.
8 miles
12. The drawing for a right triangular roof truss, represented by ΔABC is shown in
the accompanying diagram. If ≮ABC is a right angle, altitude BD = 4 meters,
and DC is 6 meters longer than AD, find the length of base AC in meters.
AC = 10 m
13.In right ∆ABC, angle C is a right angle. Altitude CD is drawn on hypotenuse
AB so that AB = 15, and AD = 3. Find CD and AB.
CD = 6
14. Right triangle DEC is inscribed in a circle with radius AC = 5. DC is a
diameter of the circle, EF is an altitude of ΔDEC, and DE = 6. Find the lengths
x and y.
E
6
D
y
y = 3.6
x
F
x = 4.8
5
A
C
15. In right triangle ABC below, CD is the altitude to hypotenuse AB. If CD = 6
and the ratio of AD to AB is 1:5, determine and state the length of BD.
BD = 12
x
4x
Name_____________________
CC Geometry H
Date _____________________
HW #19
1. Find, in simplest radical form, the length of the hypotenuse of a right triangle
whose legs have length 50 and 100.
2. Find x.
4. Find x.
6. Find SQ.
3. Find CD.
5. Find x.
7. Given right triangle ABC with altitude CD,
find AD, BD, AB and DC.
OVER
8. Write the answer in simplest radical form. Denominators should be rationalized.
a. √98 - √18
b.
c.
d.
e.
f.
g.
h.
i.
9. Using a compass and straightedge, construct a line perpendicular to
line l at point P. [Leave all construction marks.]
l
P
10. Find the measure of BC.
A
8
2
B
x­5
D
2x+1
C