BELLRINGER

x + 2

4x – 20

2x + 2

A

B

C

What is the angle measure of ∠B ?

USE TRIANGLE ANGLE SUM!

∠A + ∠B + ∠C = 180° 4x – 20 + 2x + 2 + x + 2 = 180

7x – 16 = 180

7x = 196 x = 196/7 = 28.

We want ∠B!

∠B = 2x + 2.

x =28,

so,

∠B = 2(28) + 2 = 58°!

HOW do we know that the sum of EVERY triangle must be 180° ? ? ? HINT: The answer is not because Mr. Coen

says so—you need to PROVE that this is true.

OBSERVE:

1

2 3

Supposedly, ∠1 + ∠2 + ∠3 = 180.

WHAT IF?

2 3A I A

A I A

∠1, ∠2, and ∠3 lie on a straight line—thus, their sum MUST be 180°. This situation occurs for every triangle!! That’s why every angle in a triangle must add up to 180° !

2 NEW conjectures about Isosceles Triangles

FIRST, some definitions:

LEGLEG

BASE

VERTEX ANGLE

BASE ANGLE BASE ANGLE

Conjectures:

The legs of an isosceles triangle are congruent. (We already knew this one!)

The base angles (those angles opposite of the congruent legs) are congruent.

The bisector of the vertex angle, is the perpendicular bisector of the base.

See sketchpad example.

Example 1

88°

x7 cm

y

x = ?

y = ?

Because the triangle is isosceles, the base angles are congruent. Therefore,

88 + x + x = 180

88 + 2x = 180

-88 -88

2x = 92 x = 92/2 = 46°

Certainly, y = 7cm since the triangle is isosceles!

x

Triangle is isosceles

Example 2

140°

20°

13 ftx

y°

x = ?

y = ?

First, use the triangle angle sum theorem to determine the angle measure of y.

140 + 20 + y = 180.

160 + y = 180

-160 -160

y = 20°

Since the base angles are congruent, the triangle is isosceles.

Thus, the two legs must be congruent. This means x must be 13 feet!

Exercises!

In the blue textbooks, do the following: Page 201 and 202, #2, 4, 5, 6, 8 Page 206 and 207, #1-7