Bellwork Are these triangles congruent? How? 1 2 1 2 34 34 Clickers.

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Presentation transcript:

Bellwork Are these triangles congruent? How? Clickers

Bellwork Are these triangles congruent? How? 1 Clickers

Bellwork Are these triangles congruent? How? Clickers

Bellwork Are these triangles congruent? How? Clickers

Bellwork Are these triangles congruent? How? Clickers

Use Isosceles and Equilateral Triangles Section 4.7

Going out of order Chapter 4 Test next Tuesday

The Concept Up until now in this chapter we’ve primarily been dealing with triangle congruence in any triangle Up until now in this chapter we’ve primarily been dealing with triangle congruence in any triangle Today we’re going to look at a couple of special scenarios and triangles were we can use our understanding of congruence Today we’re going to look at a couple of special scenarios and triangles were we can use our understanding of congruence

Swing Sets A typical swingset looks like this…. Vertex Axis of symmetry You’ll notice that the triangle formed by the supporting legs on each side is done that way to evenly distribute the force of the swinging? What kind of triangle is formed? What can we figure out about the angles that are formed?

Theorems Theorem 4.7: Base Angles Theorem If two sides of a triangle are congruent, then the angles opposite them are congruent Theorem 4.8: Converse of Base Angles Theorem If two angles of a triangle are congruent, then the sides opposite them are congruent Vertex Axis of symmetry

Example Vertex Axis of symmetry Solve for x 6x42

On your own Vertex Axis of symmetry Solve for x 9x63

On your own Vertex Axis of symmetry Solve for x 5x+681

On your own Vertex Axis of symmetry Solve for x 4x-523

On your own Vertex Axis of symmetry Solve for x 5x+6 18

Extensions What happens to this theorem if we extend it to an equilateral triangle? Vertex Axis of symmetry If we rotate the triangle around three times, we create an equilateral triangle, and get these Theorems Corollary to the Base Angles Theorem If a triangle is equilateral, then it is equiangular Corollary to the Converse of the Base Angles Theorem If a triangle is equiangular, then it is equilateral

On your own Vertex Axis of symmetry Solve for x 3x+425

On your own Vertex Axis of symmetry Solve for x 5x40

On your own Vertex Axis of symmetry Solve for x 6x

Homework , 19-22, 27, 28, 30, , 19-22, 27, 28, 30, 31

On your own Vertex Axis of symmetry Solve for x 50 4x-3

Most Important Points Theorems for Isosceles Triangles Theorems for Isosceles Triangles Theorems for Equilateral Triangles Theorems for Equilateral Triangles