Transcript 4.6 - MrsSicasMathWiki

4.6
Isosceles, Equilateral, & Right Triangles
HMWK:
p. 232, #s 4 – 18
p. 240, #17 – 25, 33, 34 (two proofs)
Game Plan:
Today I will be able to use congruent triangles to plan and
write proofs.
Today I will be able to apply properties of isosceles,
equilateral & right triangles to determine measures and
prove congruent triangles.
Warm-up:
Given  PQS  WXY. List all corresponding parts
of the congruent triangles.
4.6
Isosceles, Equilateral, & Right Triangles
CPCTC
• CPCTC: Corresponding Parts of Congruent
Triangles are Congruent.
why? …
In order to have congruent triangles all
corresponding parts of the triangle must be
congruent.
so …
4.6
Isosceles, Equilateral, & Right Triangles
Proofs
4.6
Isosceles, Equilateral, & Right Triangles
Proofs
4.6
Isosceles, Equilateral, & Right Triangles
Proofs
4.6
Isosceles, Equilateral, & Right Triangles
HMWK:
p. 240, #17 – 25, 33, 34 (two proofs)
Game Plan:
Today I will be able to apply properties of isosceles,
equilateral & right triangles to determine measures and
prove congruent triangles.
Warm-up:
How many acute, obtuse, and right angles does each
triangle have?
1. Acute triangle
2. Right triangle
3. Obtuse triangle
4. Equilateral triangle
4.6
Isosceles, Equilateral, & Right Triangles
Remember
Isosceles
Triangle
Right
Triangle
4.6
Isosceles, Equilateral, & Right Triangles
Isosceles Triangles
Base Angle Thm: If two sides of a triangle
are congruent, then the angles opposite
them are congruent.
Converse Base Angle Thm: If two angles of
a triangle are congruent, then the sides
opposite them are congruent.
4.6
Isosceles, Equilateral, & Right Triangles
Equilateral Triangles
Corollary: If a triangle is
equilateral, then it is
equiangular.
Corollary: If a triangle is
equiangular, then it is
equilateral.
4.6
Isosceles, Equilateral, & Right Triangles
Right Triangles
Hypotenuse-Leg (HL) Thm: If the
hypotenuse and a leg of a right triangle are
congruent to the hypotenuse and a leg of a
second right triangle, then the two triangles
are congruent.
4.6
Isosceles, Equilateral, & Right Triangles
Wrap-Up
We now have five different methods to prove
triangles are congruent. List all 5 ways.
SSS, SAS, ASA, AAS, HL
Looking at …
•Quiz 4.1 – 4.1 on Friday
•Test on Chapter 4 next Tuesday.