Triangle Angle Sum Theorem Isosceles Triangles Equilateral Triangle.

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Presentation transcript:

Triangle Angle Sum Theorem Isosceles Triangles Equilateral Triangle

Triangle Angle Sum Theorem

Definition Isosceles Triangle Tick marks indicate that the legs are congruent. They also indicate that the base angles are congruent.

Example 1 – Triangle Angle Sum Suppose that Angle G measures 40 degrees and Angle GKJ measures 80 degrees, what is the measurement of Angle J?

Example 1 – Triangle Angle Sum

Example 2

Example 3 Compute the measure of the base angles.

Example 3 Compute the measure of the base angles. AC B

Example 3 Compute the measure of the base angles. Which are the base angles? AC B

Example 3 Compute the measure of the base angles. Which are the base angles? AC B

Example 3 Compute the measure of the base angles. Which are the base angles? What may be said about the base angles? AC B

Example 3 Compute the measure of the base angles. Which are the base angles? What may be said about the base angles? AC B

Example 3 Compute the measure of the base angles. Which are the base angles? What may be said about the base angles? Since is isosceles. AC B

Example 3 Compute the measure of the base angles. Which are the base angles? What may be said about the base angles? Since is isosceles. By the Triangle Angle Sum Theorem we may write: AC B

Example 3 Compute the measure of the base angles. Which are the base angles? What may be said about the base angles? Since is isosceles. By the Triangle Angle Sum Theorem we may write: AC B

Example 3 Compute the measure of the base angles. Which are the base angles? What may be said about the base angles? Since is isosceles. By the Triangle Angle Sum Theorem we may write: AC B

Example 3, Continued

Recall the question is: Compute the measure of the base angles.

Example 3, Final Steps Recall:

Example 3, Final Steps Recall:

Example 3, Final Steps Recall:

Example 3, Final Steps Recall:

Example 3, Final Steps Recall:

Example 3, Final Steps Recall: Thus, the measurement of angle A is 62 degrees.

Equilateral Triangle A triangle with three congruent sides is said to be equilateral. Additionally, the following applies to equilateral triangles

HW