Isosceles, Equilateral, and Right Triangles
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Transcript of Isosceles, Equilateral, and Right Triangles
Isosceles Triangle Theorem
Isosceles The 2 Base s are • Base angles are the angles opposite the equal
sides.
Sample ProblemSolve for the variables• mA = 32°• mB = (4y)° • mC = (6x +2)°
A C
B
6x + 2 = 32
6x = 30
x = 5
32 + 32 + 4y = 180
4y + 64 = 180
4y = 116
y = 29
1. A
2. B
3. C
4. D
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A B C D
A. Which statement correctly names two congruent angles?
A.
B.
C.
D.
1. A
2. B
3. C
4. D
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A B C D
B. Which statement correctly names two congruent segments?
A.
B.
C.
D.
Answer: 105
Use Properties of Equilateral Triangles
Subtraction
Linear pair Thm.
Substitution
A. A
B. B
C. C
D. D A B C D
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A. x = 15
B. x = 30
C. x = 60
D. x = 90
Don’t be an ASS!!!• Angle Side Side does not work!!!
– (Neither does ASS backward!)
• It can not distinguish between the two different triangles shown below.
However, if the angle is a right angle, then they are no longer called sides. They are called…
Hypotenuse-Leg Theorem
• If the hypotenuse and one leg of a right triangle are congruent to the corresponding parts in another right triangle, then the triangles are congruent.
Prove XMZ YMZ
X Y
Z
M
Step Reason
YZXZ Given
XYZM GivenmZMX = mZMY = 90o Def of lines
ZMZM Reflexive
HL Thm
ZMX ZMY
Corresponding Parts Corresponding Parts of Congruent Triangles of Congruent Triangles are Congruentare Congruent
Given Given ΔΔABC ABC ΔΔXYZXYZ You can state that:You can state that:
A A XX B B YY C C ZZ
AB AB XY XY BCBC YZYZ CACA ZXZX
CA
CBAD
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Suppose you know that ABD CDB by SAS Thm. Which additional pairs of sides and angles can be found congruent using Corr. Parts of s are ?
Complete the following two-column proof.
Proof:
4.
ReasonsStatements
1. Given
2. Isosceles Δ Theorem
1.
2.
3. 3. Given
4. Def. of midpoint
A. A
B. B
C. C
D. D
A B C D
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Proof:
4.
ReasonsStatements
4. Def. of midpoint
5. ______
6. 6. ?
5. ΔABC ΔADC ?
Complete the following two-column proof.
SAS Thm.Corr. Parts of s are