**Section 4.2 - 4.6**

Congruency Shortcuts

Converse of the Isosceles Triangle Conjecture

Isosceles Triangle Conjecture

If a triangle is isosceles, then the base angles are congruent.

Isosceles Triangles

Any triangle with two congruent angles must be congruent

If a triangle is equilateral, then it is also equiangular. And conversely, if a triangle if equiangular, then it is also equilateral.

Equilateral and Equiangular Triangle Conjecture

ROUND 1

Worth 1 point

**Section 4.2**

Section 4.3

Triangle Inequalities

Triangle Inequality Conjecture

The sum of the two sides of a triangle must be

greater

than third side

Side Angle Inequality Conjecture

In a triangle the greatest angle across from the greatest side... the second greatest angle across the medium side... and the smallest angle across from the smallest side.

The measure of an exterior angle of a triangle is equal to the measure of the two angles that are not linear to the exterior angle.

Triangle Exterior Angle Conjecture

angle d is congruent to angle a + angle c

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

Third Angle Conjecture

Arrange sides in order from greatest to least

ROUND #2

Worth 2 points

AAA Congruency Shortcut

SSS Congruency Shortcut

SAS Congruency Shortcut

AAS Congruency Shortcut

SSA Congruency Shortcut

Congruency Shortcuts Question

Congruency Shortcuts Question

Congruency Shortcuts Question

Congruency Shortcuts Question

Congruency Shortcuts Question

Congruency Shortcuts Question

These two triangles are congruent, what congruency shortcut proves this?

These two triangles are congruent, what congruency shortcut proves this?

These two triangles are congruent, what congruency shortcut proves this?

Worth 1 point

Worth 1 point

Worth 1 point

These two triangles are congruent, what congruency shortcut proves this?

Worth 1 point

Worth 2 points

Worth 1 point

CPCTC

(Corresponding Parts of Congruent Triangles are Congruent)

The definition of congruent triangles states that if two triangles are congruent, then the corresponding parts of those congruent triangles are congruent.

If you use a congruence shortcut to show that two triangles are congruent, then you can use CPCTC to show that any of their corresponding parts are congruent.

**Rules**

Paragraph Proof: Show that line AE is congruent to line BD:

In Triangle ABD and Triangle BAE, Triangle D is congruent to Angle E and Angle B is congruent to Angle A. Also, Line AB is congruent to Line BA because they are the same segment. So Triangle ABD is congruent to Triangle BAE by SAA. By CPCTC, Line AE is congruent to Line BD.

After each mini-lesson, there will be a problem for you individually to solve on a piece of scratch paper.

The first student to raise their hand and correctly answer the question will be awarded one piece of candy for a correct answer.

The student with the most points at the end of the presentation will be awarded one bonus piece candy

Worth 1 point

Worth 2 points

**COMIC:**

ASA Congruency Shortcut

**Project by: Gautham Arunkumar and Jay Deshpande**

**Some images and definitions in this presentation are from the Third Edition of Discovering Geometry by the Kendall Hunt Publishing Company.**