Unit 7.4 Similarity in Right TrianglesLearning Goal: To find and use relationships in

similar right triangles

Warm-Up

ΔDAC ΔDCB ΔCAB

Corollary 1 to Theorem 7-3

If… C

A D B

Then…

AD = CD

CD DB

• Corollary

The length of the altitude to the

hypotenuse of a right triangle is

the geometric mean of the lengths

of the segments of the hypotenuse.

4

2

8Segments of hypotenuse

2

4

4

8=

Altitude to hypotenuse

Example

Corollary 2 to Theorem 7-3

If… C

A D B

Then…

AB = AC and AB = CB

AC AD CB DB

• Corollary

The altitude to the hypotenuse of a

right triangle separates the hypotenuse

so that the length of each leg of the

triangle is the geometric mean of the

length of the hypotenuse and the length

of the segment of the hypotenuse

adjacent to the leg.

1 4Hypotenuse 4

2

2

1=

Leg

Example

2 Segment of hypotenuse adjacent to leg

Find the geometric mean for each pair of numbers. 1. 4 and 9 2. 3 and 18 3. 5 and 9 4. 9 and 16 5. 5 and 80 6. 8 and 32

Find the value of the variables.13. 8.

9. 10.

6 ≈7.3 ≈6.7

12 20 16

x≈2.2y=2z≈4.5

x≈8.4y≈4.6z≈5.5

x=65y=60z=156

x=6y≈4.5z≈6.7

SCORE LEARNING GOALS ACHIEVED

4“I CAN TEACH IT!”

•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.

3“GOT IT…Yes!”

•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.

2“ALMOST! Yes, but…”

•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.

1“GETTING THERE….No, but…”

•I am able to identify similar right triangles.•I answered 5 practice questions correctly.

0“CLUELESS… No idea”

•I have NO idea what you are talking about.•“WHAT????”•I answered fewer than 5 practice questions correctly.

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.

We’re done.(Except…)

Pages 464-465

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