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Use Similar Right Triangles Ch 7.3

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Page 1: Use Similar Right Triangles Ch 7.3. Similar Right Triangle Theorem If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles

Use Similar Right Triangles

Ch 7.3

Page 2: Use Similar Right Triangles Ch 7.3. Similar Right Triangle Theorem If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles

Similar Right Triangle Theorem

• If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original right triangle.

Page 3: Use Similar Right Triangles Ch 7.3. Similar Right Triangle Theorem If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles

How do you names the 3 similar triangles?

1. Draw the smallest triangle.

îSUT ~ îTUR

2. Draw the middle triangle.3. Draw the largest triangle.

~ îSTR

4. Match up the angles.

Page 4: Use Similar Right Triangles Ch 7.3. Similar Right Triangle Theorem If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles

Name the similar triangles, then find x.îEHG ~ îGHF ~ îEGF

45

3 xGF

GH

EF

EG

5

12

125

x

x

To find x make a ratio of the hypotenuses and the a ratio of 2 proportional legs.

Page 5: Use Similar Right Triangles Ch 7.3. Similar Right Triangle Theorem If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles

Name the similar triangles and find x.îLKM ~ îMKJ ~ îLMJ

sideLongestnd

Hypotenuse

2

KM

LM

JM

JL

x

5

12

13

6013 x

13

60x

Page 6: Use Similar Right Triangles Ch 7.3. Similar Right Triangle Theorem If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles

Find x and y.

2172

x

y

222 cba 222 7221 c

25182441 c25625 c

c75

longest

Hypnd2

CD

CB

AC

AB

y

21

72

75

151275 y16.20y

222 7216.20 x

12.69x

Page 7: Use Similar Right Triangles Ch 7.3. Similar Right Triangle Theorem If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles

Find x.

12

3 x

x

362 x

362 x

6x

longest

Shortestnd2

Page 8: Use Similar Right Triangles Ch 7.3. Similar Right Triangle Theorem If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles

Find xx

x 4

5

202 x

52

225

45

202

x

Page 9: Use Similar Right Triangles Ch 7.3. Similar Right Triangle Theorem If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles

Theorem 7.6

• In a right triangle the altitude from the right angle to the hypotenuse divides the hypotenuse into 2 segments.

• The length of the altitude is the geometric mean of the lengths of the 2 segments

DBADCD CD

DB

AD

CD

Page 10: Use Similar Right Triangles Ch 7.3. Similar Right Triangle Theorem If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles

41682 y

Page 11: Use Similar Right Triangles Ch 7.3. Similar Right Triangle Theorem If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles

48 x

22 )4(8 x

x464

x16

Page 12: Use Similar Right Triangles Ch 7.3. Similar Right Triangle Theorem If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles

Finding the length of the altitude

B

C A

D1.Set up a proportion to find

BD.2. Find side AD.3. Plug values into

DBADCD

Page 13: Use Similar Right Triangles Ch 7.3. Similar Right Triangle Theorem If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles

Finding the length of the altitude.

deSmallestSiTriangleSmallest

HypotenuseTriangleSmallest

deSmallestSiTriangleBig

HypotenuseTriangleBig

x

18

18

30

32430

)18)(18(30

x

x

8.10x

10.8

2.198.1030

19.2

8.102.19 Altitude 4.1436.207

Page 14: Use Similar Right Triangles Ch 7.3. Similar Right Triangle Theorem If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles

Finding the length of the altitude.

deSmallestSiTriangleSmallest

HypotenuseTriangleSmallest

deSmallestSiTriangleBig

HypotenuseTriangleBig

x

6

6

56

3656

)6)(6(56

x

x

7.2x

2.7

7.107.256

10.7

7.27.10 Altitude 3.589.28

Page 15: Use Similar Right Triangles Ch 7.3. Similar Right Triangle Theorem If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles

Finding the length of the altitude.

deSmallestSiTriangleSmallest

HypotenuseTriangleSmallest

deSmallestSiTriangleBig

HypotenuseTriangleBig

x

15

15

613

225613

)15)(15(613

x

x

6.9x

9.6

8.136.9613

13.8

6.98.13 Altitude 5.1148.132

Page 16: Use Similar Right Triangles Ch 7.3. Similar Right Triangle Theorem If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles

Find the amplitude, if these are right triangles. One of these is not a right

triangle

8.5 6.6

not right

Page 17: Use Similar Right Triangles Ch 7.3. Similar Right Triangle Theorem If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles

Theorem 7.7• In a right triangle, the altitude divides the

hypotenuse into 2 segments.

• The length of each leg of each right triangle is the geometric mean of length of the hypotenuse and a segment of the hypotenuse

ADABAC

DBABCB

Page 18: Use Similar Right Triangles Ch 7.3. Similar Right Triangle Theorem If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles

Find x and y

4.2512.75

xy

DBABCB

ADABAC

25.417CB5.825.72 CB

75.1217AC7.1475.216 AC

Page 19: Use Similar Right Triangles Ch 7.3. Similar Right Triangle Theorem If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles

Find x

28x

16x

4x

Page 20: Use Similar Right Triangles Ch 7.3. Similar Right Triangle Theorem If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles

Find x and y

28

x +2y

DBADCD

ADABAC

282 x162 x

810AC9.880 AC

42 x2x

Page 21: Use Similar Right Triangles Ch 7.3. Similar Right Triangle Theorem If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles

Find a

Page 22: Use Similar Right Triangles Ch 7.3. Similar Right Triangle Theorem If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles

Find b

Page 23: Use Similar Right Triangles Ch 7.3. Similar Right Triangle Theorem If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles
Page 24: Use Similar Right Triangles Ch 7.3. Similar Right Triangle Theorem If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles

Find x and y

yx|--------- 34 -------------|

30z

16


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