+ All Categories
Transcript
Page 1: [PPT]Isosceles, Equilateral, and Right Triangles · Web viewIsosceles, Equilateral, and Right Triangles Chapter 4.6 Isosceles Triangle Theorem Isosceles The 2 Base s are Base angles

Isosceles, Equilateral, and Right Triangles

Chapter 4.6

Page 2: [PPT]Isosceles, Equilateral, and Right Triangles · Web viewIsosceles, Equilateral, and Right Triangles Chapter 4.6 Isosceles Triangle Theorem Isosceles The 2 Base s are Base angles

Isosceles Triangle Theorem

Isosceles The 2 Base s are • Base angles are the angles opposite the equal

sides.

Page 3: [PPT]Isosceles, Equilateral, and Right Triangles · Web viewIsosceles, Equilateral, and Right Triangles Chapter 4.6 Isosceles Triangle Theorem Isosceles The 2 Base s are Base angles

Isosceles Triangle Theorem

A C

B

If AB BC, then A C

Page 4: [PPT]Isosceles, Equilateral, and Right Triangles · Web viewIsosceles, Equilateral, and Right Triangles Chapter 4.6 Isosceles Triangle Theorem Isosceles The 2 Base s are Base angles

Isosceles Triangle Theorem

A C

B

If A C then AB BC

Page 5: [PPT]Isosceles, Equilateral, and Right Triangles · Web viewIsosceles, Equilateral, and Right Triangles Chapter 4.6 Isosceles Triangle Theorem Isosceles The 2 Base s are Base angles

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

Page 6: [PPT]Isosceles, Equilateral, and Right Triangles · Web viewIsosceles, Equilateral, and Right Triangles Chapter 4.6 Isosceles Triangle Theorem Isosceles The 2 Base s are Base angles

Find the Measure of a Missing Angle

120o

180o – 120o = 60o

30o 30o

30o

180o – 30o = 150o

75o

75o

Page 7: [PPT]Isosceles, Equilateral, and Right Triangles · Web viewIsosceles, Equilateral, and Right Triangles Chapter 4.6 Isosceles Triangle Theorem Isosceles The 2 Base s are Base angles

1. A2. B3. C4. D

A. 25

B. 35

C. 50

D. 130

Page 8: [PPT]Isosceles, Equilateral, and Right Triangles · Web viewIsosceles, Equilateral, and Right Triangles Chapter 4.6 Isosceles Triangle Theorem Isosceles The 2 Base s are Base angles

1. A2. B3. C4. D

0%0%0%0%

A B C D

A. Which statement correctly names two congruent angles?

A.

B.

C.

D.

Page 9: [PPT]Isosceles, Equilateral, and Right Triangles · Web viewIsosceles, Equilateral, and Right Triangles Chapter 4.6 Isosceles Triangle Theorem Isosceles The 2 Base s are Base angles

1. A2. B3. C4. D

0%0%0%0%

A B C D

B. Which statement correctly names two congruent segments?

A.

B.

C.

D.

Page 10: [PPT]Isosceles, Equilateral, and Right Triangles · Web viewIsosceles, Equilateral, and Right Triangles Chapter 4.6 Isosceles Triangle Theorem Isosceles The 2 Base s are Base angles

Equilateral Triangle Theorem

Equilateral Equiangular

Each angle = 60o !!!

60

3180

Page 11: [PPT]Isosceles, Equilateral, and Right Triangles · Web viewIsosceles, Equilateral, and Right Triangles Chapter 4.6 Isosceles Triangle Theorem Isosceles The 2 Base s are Base angles

Answer: 105

Use Properties of Equilateral Triangles

Subtraction

Linear pair Thm.

Substitution

Page 12: [PPT]Isosceles, Equilateral, and Right Triangles · Web viewIsosceles, Equilateral, and Right Triangles Chapter 4.6 Isosceles Triangle Theorem Isosceles The 2 Base s are Base angles

A. AB. BC. CD. D A B C D

0% 0%0%0%

A. x = 15

B. x = 30

C. x = 60

D. x = 90

Page 13: [PPT]Isosceles, Equilateral, and Right Triangles · Web viewIsosceles, Equilateral, and Right Triangles Chapter 4.6 Isosceles Triangle Theorem Isosceles The 2 Base s are Base angles

A. AB. BC. CD. D

A B C D

0% 0%0%0%

A. 30

B. 60

C. 90

D. 120

Page 14: [PPT]Isosceles, Equilateral, and Right Triangles · Web viewIsosceles, Equilateral, and Right Triangles Chapter 4.6 Isosceles Triangle Theorem Isosceles The 2 Base s are Base angles

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…

Page 15: [PPT]Isosceles, Equilateral, and Right Triangles · Web viewIsosceles, Equilateral, and Right Triangles Chapter 4.6 Isosceles Triangle Theorem Isosceles The 2 Base s are Base angles

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.

Page 16: [PPT]Isosceles, Equilateral, and Right Triangles · Web viewIsosceles, Equilateral, and Right Triangles Chapter 4.6 Isosceles Triangle Theorem Isosceles The 2 Base s are Base angles

ABC XYZ Why?HL Theorem

B

CA

X Z

Y

Page 17: [PPT]Isosceles, Equilateral, and Right Triangles · Web viewIsosceles, Equilateral, and Right Triangles Chapter 4.6 Isosceles Triangle Theorem Isosceles The 2 Base s are Base angles

Prove XMZ YMZ

X Y

Z

M

Step Reason

YZXZ GivenXYZM Given

mZMX = mZMY = 90o Def of lines

ZMZM ReflexiveHL Thm

ZMX ZMY

Page 18: [PPT]Isosceles, Equilateral, and Right Triangles · Web viewIsosceles, Equilateral, and Right Triangles Chapter 4.6 Isosceles Triangle Theorem Isosceles The 2 Base s are Base angles

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

Page 19: [PPT]Isosceles, Equilateral, and Right Triangles · Web viewIsosceles, Equilateral, and Right Triangles Chapter 4.6 Isosceles Triangle Theorem Isosceles The 2 Base s are Base angles

CA

CBAD

23

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 ?

Page 20: [PPT]Isosceles, Equilateral, and Right Triangles · Web viewIsosceles, Equilateral, and Right Triangles Chapter 4.6 Isosceles Triangle Theorem Isosceles The 2 Base s are Base angles

Complete the following two-column proof.

Proof:

4.

ReasonsStatements1. Given2. Isosceles Δ Theorem

1. 2.3. 3. Given

4. Def. of midpoint

Page 21: [PPT]Isosceles, Equilateral, and Right Triangles · Web viewIsosceles, Equilateral, and Right Triangles Chapter 4.6 Isosceles Triangle Theorem Isosceles The 2 Base s are Base angles

A. AB. BC. CD. D

A B C D

0% 0%0%0%

Proof:

4.

ReasonsStatements

4. Def. of midpoint5. ______

6. 6. ?5. ΔABC ΔADC ?

Complete the following two-column proof.

SAS Thm.Corr. Parts of s are

Page 22: [PPT]Isosceles, Equilateral, and Right Triangles · Web viewIsosceles, Equilateral, and Right Triangles Chapter 4.6 Isosceles Triangle Theorem Isosceles The 2 Base s are Base angles

HomeworkCh 4-6 • pg 248

1 – 10, 14 – 27, 32, 33, 37 – 39, & 48

2,

22121 yyxx

Reminder!

Midpoint Formula:

Video C


Top Related