Unit 5: Triangle Congruence
Table of Contents
- 4.1 Classifying Triangles
- 4.2 Angle Relationships in Triangles
- Triangle Angle Theorems
- Animation 171
- Triangle Angle Theorems (V2)
- Animation 2
- Triangle Angle Theorems (V3)
- Transformation Proof 3
- 4.3 Congruent Triangles
- Proving Tri's Congruent (I)
- Proving Tri's Congruent (II)
- 4.4 Triangle Congruence: SSS and SAS
- SAS - Exercise 1A
- SAS - Exercise 1B
- SAS - Exercise 2
- SAS - Exercise 3
- SSS: Exercise 1
- SAS: Dynamic Proof!
- Animation 136
- SSS: Dynamic Proof!
- SSS: Dynamically Illustrated
- Animation 138
- SSA Theorem?
- Is "SSA" Legit? What Do You Think?
- 4.5 Triangle Congruence: ASA, AAS, and HL
- ASA Theorem?
- Animation 137
- HL: Hypotenuse-Leg Action!
- Animation 225
- Congruent Triangles 1
- Congruent Triangles 2
- Congruent Triangles 3
- Congruent Triangles 4
- Congruent Triangles 5
- Congruent Triangles 6
- Congruent Triangles 7
- 4.6 Triangle Congruence: CPCTC
- 4.7 Introduction to Coordinate Proof
- 4.8 Isosceles and Equilateral Triangles
Triangle Angle Theorems
Interact with the app below for a few minutes. [br]Then, answer the questions that follow. [br][br]Be sure to change the locations of this triangle's vertices each time [i]before[/i] you drag the slider!
What is the [b]sum of the measures of the interior angles of this triangle? [/b]
What is the [b]sum of the measures of the exterior angles [/b]of this triangle?
Proving Tri's Congruent (I)
[color=#000000]Recall an [b]isometry[/b] is a [b]transformation that preserves distance. [br][/b][br]Also recall that, by definition, 2 polygons are said to be congruent polygons if and only if one polygon can be mapped perfectly onto the other polygon using an isometry or a composition of two or more isometries. [br][br]Use the tools of GeoGebra to show, by definition, that the following two triangles are congruent. [/color]
SAS - Exercise 1A
In the applet below, use the tools of transformational geometry to informally demonstrate the SAS Triangle Theorem to be true. [br][br]That is, use the tools of transformational geometry to map the [color=#bf9000][b]yellow triangle[/b][/color] onto the empty triangle. [br][br]Before starting, feel free to adjust any aspect of the [color=#bf9000][b]starting triangle[/b][/color] ([color=#666666][b]tilt[/b][/color], [color=#1e84cc][b]size of the included angle[/b][/color], [b]and the positions of points [/b][i]A[/i][b], [/b][i]B[/i][b], and [/b][i]C[/i]). You can also use the [b]black slider[/b] to [b]change the position of the image (empty) triangle.[/b] [br][br][i]Once you do start, it is recommended that you don't readjust these parameters. [/i]
Question:
Describe how you know the two triangle are congruent.
ASA Theorem?
[color=#000000]Suppose 2 triangles have 2 pairs of congruent angles. Suppose we also know that the side between each set of given angles (in one triangle) is congruent to the side between this same pair of angles in the other triangle. [br][br]Does knowing only this constitute sufficient evidence to prove the triangles congruent? If so, explain how/why with respect to the transformations and/or triangle congruence theorems you've previously learned. If not, clearly explain why not. [/color]