4-6 Isosceles Triangles

Before We Begin…

• Mr. A was wrong. The A-Team van was a GMC model, part of General Motors, of which Chevrolet is a subsidiary.

Isosceles Triangle Theorem: if two sides of a triangle are congruent, then the angles opposite of those sides are congruent.

The opposite is true, too!

A triangle is equilateral if and only if it is equiangular

Since all angles=180°,

then every angle in an equilateral triangle is 60°

60°

60°60°

• That’s It.

• Just use these ideas to find Scooby Doo Clues.

4-7 Triangles and Coordinate Proofs

Don’t worry, this is different!

(0,0)

(4,8)

(8,0)x

y

0

A

B

C

∆ABC is isosceles

(4, ?)

Name the missing coordinates.

(?, 6)

(?,?)(0,0)

(2,6)

(4,0)

0

y

x

• Draw and label an isosceles triangle with base that is a units long, and b units tall.

(0,0) (a,0)

(½a, b)y

x0

If you don’t know the value, or cannot find it, just use a new letter.

Draw an isosceles triangle with a base that is 2a long.

(0,0) (2a,0)

(a, )by

x0

Name the missing coordinates

(1,0)(-1,0)

(0,a)

A coordinate proof involves drawing a picture on a graph, and using the distance formula, midpoint formula, and algebra to prove things.

HINT: When drawinga coordinate proof, always use the ORIGIN as a midpoint or vertex !

WHY?

because (0,0) is easy to work with in the distance formula!

• Let’s try some together!