8. Corollary 1 to Theorem 7-3
• Corollary
The length of the altitude to the
If… C
hypotenuse of a right triangle is
the geometric mean of the lengths
of the segments of the hypotenuse.
A D B
Then…
Example
2 AD = CD
CD DB
8
Segments of 2 4 Altitude to
4 hypotenuse = hypotenuse
4 8
9. Corollary 2 to Theorem 7-3
• Corollary
The altitude to the hypotenuse of a
right triangle separates the hypotenuse If… C
so that the length of each leg of the
triangle is the geometric mean of the
length of the hypotenuse and the length
A D B
of the segment of the hypotenuse
adjacent to the leg. Then…
Example AB = AC and AB = CB
AC AD CB DB
1 4
Hypotenuse 4 2 Leg
=
2 2 1 Segment of
hypotenuse
adjacent to leg
10. Find the geometric mean for each pair of numbers.
1. 4 and 9 2. 3 and 18 3. 5 and 9
6 ≈7.3 ≈6.7
4. 9 and 16 5. 5 and 80 6. 8 and 32
12 20 16
Find the value of the variables.
13. 8.
x≈8.4
x≈2.2 y≈4.6
y=2 z≈5.5
z≈4.5
9. 10.
x=65 x=6
y=60 y≈4.5
z=156 z≈6.7
11. LEARNING GOALS SCALE - Unit 7-4: Similarity in Right Triangles
•Students will be able to identify corresponding parts of similar right triangles.
•Students will understand and be able to understand Theorem 7-3 and its corollaries.
SCORE LEARNING GOALS ACHIEVED
“I CAN TEACH IT!”
4 •I am able to identify similar right triangles.
•I understand and can use Theorem 7-3.
•I understand and can use the Corollaries to Theorem 7-3.
•I answered all practice questions correctly.
•I am able to help other students achieve the learning goals.
“GOT IT…Yes!”
3 •I am able to identify similar right triangles.
•I understand or can use Theorem 7-3.
•I understand or can use the Corollaries to Theorem 7-3.
•I answered 8 or 9 practice questions correctly.
“ALMOST! Yes, but…”
2 •I am able to identify similar right triangles.
•I understand Theorem 7-3.
•I understand the Corollaries to Theorem 7-3.
•I answered 6 or 7 practice questions correctly.
“GETTING THERE….No, but…”
1 •I am able to identify similar right triangles.
•I answered 5 practice questions correctly.
“CLUELESS… No idea”
0 •I have NO idea what you are talking about.
•“WHAT????”
•I answered fewer than 5 practice questions correctly.
