T3.L2 Proving Triangle Congruence Theorem

Proving Triangle

Congruence Theorem

TEKS: Geom.6B | Prove two triangles are congruent by applying the Side-Angle-Side,
Angle-Side-Angle, Side-Side-Side, Angle-Angle-Side, and Hypotenuse-Leg congruence
conditions.

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

Multiple Select

Which congruency statements match the following picture.

• $$\angle SRT\cong\angle XWB$$

• $$\angle TWR\cong\angle XRT$$

• $$\angle WXB\cong\angle RTS$$

• $$\angle WSB\cong\angle TWX$$

Multiple Select

Which congruency statements match the following picture.

• $$\overline{DT\ }$$ $$\cong$$ $$\overline{DZ}$$

• $$\angle TDM\ \cong\angle DZC$$

• $$\angle TZC\ \cong\angle TCZ$$

• $$\overline{TC}$$ $$\cong$$ $$\overline{TZ}$$

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)

Match

Place the pictures in the correct proof category.

Isometry Definition

Reflection Definition

Perpendicular Bisector Theorem

• Isometry Definition

• Reflection Definition

• Perpendicular Bisector Theorem

Side-Side-Side Theorem

Multiple Select

Which set of figures cannot be proved congruent using Side-Side-Side Congruence Theorem.

Side-Angle-Side Theorem

Dropdown

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Select answer

congruence theorem can be used to prove that Triangle ABC ≅ Triangle DEF

Angle-Side-Angle Theorem

Hyptenuse-Leg Theorem

Match

Match the following

Side-Side-Side

Side-Angle-Side

Angle-Side-Angle

Hypotenuse-Leg

• Side-Side-Side

• Side-Angle-Side

• Angle-Side-Angle

• Hypotenuse-Leg

Open Ended

Essential Question

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