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Triangle Review

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A scalene triangle has no sides and no angles equal.

An isosceles triangle has two sides and two angles equal.

An equilateral triangle has three sides and three angles equal.

Triangle Review

A right triangle has one right angle.

Identify the triangle below;

right isosceles

How are the three sides of a right triangle related to each other?

The Pythagorean Theorem

a2 + b2 = c2

c

Hypotenuse, the longest side of a right triangle

a

b

c

8

6

Example 1: Calculate side c.

c2 = a2 + b2

c2 = 82 + 62

c2 = 64+ 36

c2 = 100

c = 10

hypotenuse

Example 2: Calculate side x.

a2 + b2 = c2

x

7

x2 + 72 = 122

x2 + 49 = 144

12

x2 = 144 – 49

x2 = 95

x = 9.7

Similar Triangles

Two triangles are considered to be similar if and only if:

- they have the same shape

- corresponding angles are equal

- the ratio of the corresponding side lengths are equal

F

C

x

1 m

A

B

D

E

72 cm

18.5 m

Ex 1. Find x.

Step 1: Identify two similar triangles.

ABC ~ DEF

Step 2: Write equivalent ratios

F

C

x

1 m

A

B

D

E

72 cm

18.5 m

Step 4: Use the ratios that apply to solve for x.

0.72x = 18.5

x = 25.7 m

Ex #2: Surveyors have laid out triangles to find the length of a lake. Calculate this length, AB.

ft

Step 1: Draw a labeled diagram.

PROVIDED

ft

Step 2: Identify two similar triangles.

ft

ACB ~ ECD

Step 3: Write equivalent ratios

Step 4: Use the ratios that apply to solve for x.

ft

ft

ft