Download 4.6 Isosceles, Equilateral, and Right Triangles Obj. Use properties of

4.6 Isosceles, Equilateral, and Right Triangles
Obj. Use properties of isosceles and equailateral triangles
Use properties of right triangles. vertex angle
leg leg
base base angles
Base Angles Theorem ­ If two sides of a triangle are congruent, then the angles opposite them are congruent. B __ __ If AB ≡ AC, then <B ≡ <C
A
C
Converse of the Base Angles Theorem ­ If two angles of a triangle are congruent, then the side opposite them are congruent.
__ __
B
If <B ≡ <C, then AB ≡ AC
A
C
1
Corollaries: If a triangle is equilateral, then it is equilangular.
If a triangle is equiangular, then it is equilateral.
Recall that if a statement and it's converse is true, then it is a biconditional.
A triangle is equilateral iff it is equiangular. Using equilateral and isosceles triangles:
a. Find the value of x and y.
x y
b. Find the value of x and y. y x
50
2
A
__ __
Given: ABC; AB ≡ AC
Prove: <C ≡ <B
__ __
1) ABC; AB ≡ AC 1) Given
__
C D B
2) Let D be midpt of CB 2) Every segment has exactly one midpt
__
3) Draw AD
3) Through 2 points there is 1 line
4)
4)
5)
5)
6)
6)
7)
7)
3
Ways to prove triangles congruent:
1) SSS
2) SAS
3)AAS
4)ASA
5) HL
Hypotenuse Leg Congruence Theorem (HL) ­ If the hypotenuse and leg of a right triangle are congruent to the hypotenuse and leg of a second right triangle, then the two triangles are congruent. A D
__ __ __ __
If BC ≡ EF and AC ≡ DF, then
B C E F
ABC ≡ DEF
When using HL you MUST state that you have right angles or right triangles and that all right angles are congruent.
__
B F
Given: D is the midpoint of CE. <BCD an d <FED are right angles
BD ≡ FD
C D E
Prove: BCD ≡ FED
1) D is the midpoint of CE. 1) Given
<BCD an d <FED are right angles
BD ≡ FD
2)
2)
3)
3)
4)
4)
4
Assignment 4.6 page 239 8 ­ 25 all
35 & 36
Proof ­ (5 steps) __ __
Given: PS <3 Prove: <1 ≡ QR
≡ <4
≡ <2
P Q
3
4
5 6
1 2
S R
5
6