Unit 3 - 2
Key Objectives (from the notes):
- Apply SSS and SAS to construct triangles and to solve problems.
- Prove triangles congruent by using SSS and SAS.
- Apply ASA, AAS, and HL to construct triangles and to solve problems.
- Prove triangles congruent by using ASA, AAS, and HL.
Well, what do you know? I made it to the second "episode" of Triangle Land, as my best friend Grant here at Pioneer Heritage Middle School would say. But, as I am currently in a very, very serious and robust mathematics class, I must get to the point.
This entire lesson focuses on one main concept: triangle congruence. More specifically, the five ways you can prove two triangles congruent: by the SSS, SAS, ASA, AAS, and HL congruency postulates. Basically, what each one says is that if you know specific coresponding parts of two triangles are congruent, then the two triangles themselves are congruent.
This entire lesson focuses on one main concept: triangle congruence. More specifically, the five ways you can prove two triangles congruent: by the SSS, SAS, ASA, AAS, and HL congruency postulates. Basically, what each one says is that if you know specific coresponding parts of two triangles are congruent, then the two triangles themselves are congruent.
- SSS deals with the three sides: if these three parts of two triangles are congruent respectively, then the triangles are congruent.
- SAS deals with two sides an an included angle: if these three parts of two triangles are congruent respectively, then the triangles are congruent.
- ASA deals with two angles and an included side: if these three parts of two triangles are congruent respectively, then the triangles are congruent.
- AAS deals with two angles and a non-included side: if these three parts of two triangles are congruent respectively, then the triangles are congruent.
- HL deals with the hypotenuse and one leg in a right triangle: if these two parts of two right triangles are congruent respectively, then the right triangles are congruent.
To answer that question relatively quickly, yes. It does matter. Look at the two triangles on the right. A proper congruence statement would be "Triangle PRW is congruent to triangle BSM". That's because the names of each corresponding pair of points have to be in the corresponding positions when you name the triangle. Saying "Triangle PWR is congruent to triangle BSM" would not work because point W does not coincide with point S and point R does not coincide with point M.
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That about covers it for this lesson.