Isosceles Triangle ABC Vertex Angle Leg Base Angles

Isosceles Triangle ABC • Vertex Angle • Leg • Base Angles

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Theorem 4. 6 -Base Angles Theorem • If two sides of a triangle are congruent, • Then, the angles opposite them are congruent.

Prove Theorem 4. 6 • Given: • Prove:

Theorem 4. 6 -Base Angles Theorem • The converse: • If two sides of a triangle are congruent, • Then, the angles opposite them are congruent.

Theorem 4. 7 -Converse of the Base Angles Theorem • If two angles of a triangle are congruent, • Then the sides opposite them are congruent.

Prove Theorem 4. 7 • Given: • Prove:

Now that you know about these theorems…. test yourself with some problems…

Solve for x and y

Corollary to theorem 4. 6 & 4, 7 • If a triangle is equilateral, • Then it is equiangular • If a triangle is equiangular • Then it is equilateral.

Theorem 4. 8 -Hypotenuse-Leg (HL) Congruence Theorem • If the hypotenuse and leg of a right triangle are congruent to the hypotenuse and leg of a second right triangle, • Then the two triangles are congruent.

Solve for x

Write the equation of the line • Passing through P(1, 1) and • Perpendicular to y = -3 x - 4

Given the points (5, 8) & (-12, 1) • What is the distance between them? • What are the coordinates of the midpoint?

Assignment 4. 6