Using Parts of Congruent Triangles to Find x, Sides, and Angles. Exterior Angle Theorem.

You have been told that two triangles are congruent. Now, the issue is: How may you use this congruence statement to find x, and one side, or angle? Do you have to equal expressions, or you setup an equation equal to 180°?

Have you heard about the Exterior Angle Theorem? Do you know what are remote interior angles? How is the exterior angle related to the remote interior angles?

You will really enjoy working this lesson. It will show some examples about Exterior Angle Theorem, and It will present you Corresponding Parts of Congruent Triangles are Congruent, and then it builds on CPCTC to show you a set of examples like the ones above described. For each couple of examples; you will be given a multiple choice problem to solve. You will know if your answer is right, or wrong right away!

Lesson's Content

Lesson's Glossary

Acute angle
An angle whose measure is greater than 0 but less than 90 degrees.

Acute triangle
A triangle whose angles are acute.

CPCTC

Corresponding Parts of Congruent Triangles are Congruent.

Equilateral triangle
A triangle whose sides are equal in length.

Isosceles triangle
A triangle with two sides of equal length.

Obtuse angle
An angle whose measure is greater than 90 but less than 180 degrees.

Obtuse triangle
A triangle with one acute angle.

Right triangle
A triangle that has a 90 degree angle.

Scalene triangle
A triangle with no equilateral sides.

Triangle
A polygon with three sides.

Interactive Geometric Applets: Relevant Theorems.

You may drag point B and verify that the triangles keep all corresponding parts congruent.

This is what we mean by CPCTC:

Corresponding Parts of Congruent Triangles are Congruent.

Interior Angle Sum Theorem for a triangle states that

the sum of the interior angles in a triangle is always 180°.

You might try dragging any of the vertices in this applet and

check that the sum is always 180°.

The Exterior Angle Theorem for a triangle specifies that the sum of the two remote

interior angles is equal to the exterior angle for the third angle in the triangle.

You may drag any of the vertices in the triangle and verify the condition above described.

The Third Angle Theorem states that given two triangles with two pairs of congruent angles,

then the remaining third angles are also congruent. Drag the slider in the applet

to verify it.

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