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# Sections 4.2-4.6

Geometry ACC 2013
by

## Gautham Arunkumar

on 18 July 2013

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#### Transcript of Sections 4.2-4.6

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.
Full transcript