T3.L2 Proving Triangle Congruence Theorem

M1.T3.L2

LO: SWBAT prove two triangles are congruent using the Side-Side-Side (SSS), Side-Angle-Side (SAS) congruence theorems, Angle-Side-Angle (ASA), Hypothenuse-Leg (HL)

DOL: Given two triangles, students will correctly prove congruency
using the four different congruence theorems by answering in at least 7 of 9 questions correctly.

Vocabulary

1.

Side-Side-Side Congruence Theorem (SSS) - If three sides of one triangle are congruent to the corresponding sides of
another triangle, then the triangles are congruent.

2.

Side-Angle-Side Congruence Theorem (SAS) - If two sides and the included angle of one triangle are congruent to the
corresponding sides and the included angle of the second triangle, then the triangles are congruent.

3.

Angle-Side-Angle Congruence Theorem (ASA)- If two angles and the included side of one triangle are congruent to the
corresponding angles and the included side of the second triangle, then the triangles are congruent.

4.

Hypotenuse-Leg Congruence Theorem (HL)- If the hypotenuse and a leg of a right triangle are each congruent with the
corresponding hypotenuse and leg of another right triangle, then the triangles are congruent.

Essential Question

You have defined the transformations that produce isometry. What are the 3 concepts from isometry transformations that prove triangle congruence theorems?

Congruent Line Segments by Reflection
and Congruency Statements

Proving Congruency w/ Isometry

1.

Isometries preserve distances and angle measures. (Isometry Definition)

2.

Any point in the plane can be reflected across a line to map onto another point in the
plane. (Reflection Definition)

3.

A point is equidistant from two other points if and only if it lies on their perpendicular
bisector. (Perpendicular Bisector Theorem)

Side-Side-Side Theorem

Side-Angle-Side Theorem

Angle-Side-Angle Theorem

Hyptenuse-Leg Theorem