CH. 4-1 AND 4-2: APPLY TRIANGLE SUM PROPERTIES

AND CONGRUENCEMr. Schaab’s Geometry Class

Our Lady of Providence Jr.-Sr. High School

2014-2015

Triangles

A triangle is a polygon with three sides. A triangle with vertices (corners) A, B, and C

is called “triangle ABC” or “△ABC.”

Types of Triangles

Interior and Exterior Angles

A triangle’s interior angles are the three angles contained within the boundaries of the triangle.

The exterior angles of a triangle are the angles formed when the sides of the triangle are extended. They always lie outside the triangle.

Triangle Sum Theorem

The sum of the measures of the interior angles of a triangle is 180°.

Exterior Angle Theorem

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.

Congruent Triangles Congruent Figures – If two geometric

figures are congruent, then all the parts of one figure are congruent to the corresponding parts of the other figure.

In the diagram, ∠P and ∠L are corresponding angles, and JK and QR are corresponding sides.

Third Angles Theorem

If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.

In the diagram, the unlabeled angles must be congruent. What is the measure of both unlabeled angles? 73°

Properties of Congruent Triangles