objectives: use properties of isosceles and equilateral triangles use properties of right triangles
TRANSCRIPT
![Page 1: Objectives: Use properties of isosceles and equilateral triangles Use properties of right triangles](https://reader036.vdocuments.us/reader036/viewer/2022082611/56649e865503460f94b8a1d3/html5/thumbnails/1.jpg)
Objectives:
• Use properties of isosceles and equilateral triangles
• Use properties of right triangles
![Page 2: Objectives: Use properties of isosceles and equilateral triangles Use properties of right triangles](https://reader036.vdocuments.us/reader036/viewer/2022082611/56649e865503460f94b8a1d3/html5/thumbnails/2.jpg)
Properties of Isosceles Triangles• In lesson 4.1, you
learned that a triangle is an isosceles if it has at least two congruent sides.
• The two angles adjacent to the base are the base angles. The angle opposite the base is the vertex angle.
base angles
vertex angle
base
legleg
B
A C
![Page 3: Objectives: Use properties of isosceles and equilateral triangles Use properties of right triangles](https://reader036.vdocuments.us/reader036/viewer/2022082611/56649e865503460f94b8a1d3/html5/thumbnails/3.jpg)
Remember:
• An EQUILATERAL triangle is a special type of isosceles triangle.
A
B C
![Page 4: Objectives: Use properties of isosceles and equilateral triangles Use properties of right triangles](https://reader036.vdocuments.us/reader036/viewer/2022082611/56649e865503460f94b8a1d3/html5/thumbnails/4.jpg)
Equilateral and Isosceles Triangles
a. Find the value of xb. Find the value of y
3x = 180X = 60
x°
y°
![Page 5: Objectives: Use properties of isosceles and equilateral triangles Use properties of right triangles](https://reader036.vdocuments.us/reader036/viewer/2022082611/56649e865503460f94b8a1d3/html5/thumbnails/5.jpg)
Ex. 2: Using Equilateral and Isosceles Trianglesa. Find the value of xb. Find the value of y
120° + 2y° = 180°2y = 60 y = 30
x°
y°60°
![Page 6: Objectives: Use properties of isosceles and equilateral triangles Use properties of right triangles](https://reader036.vdocuments.us/reader036/viewer/2022082611/56649e865503460f94b8a1d3/html5/thumbnails/6.jpg)
Using Properties of Right Triangles
• You have learned four ways to prove that triangles are congruent.• Side-Side-Side (SSS)• Side-Angle-Side (SAS)• Angle-Side-Angle (ASA)• Angle-Angle-Side (AAS)
![Page 7: Objectives: Use properties of isosceles and equilateral triangles Use properties of right triangles](https://reader036.vdocuments.us/reader036/viewer/2022082611/56649e865503460f94b8a1d3/html5/thumbnails/7.jpg)
Solve:
Solution:Isosceles TriangleX = 180-54-54X=72
![Page 8: Objectives: Use properties of isosceles and equilateral triangles Use properties of right triangles](https://reader036.vdocuments.us/reader036/viewer/2022082611/56649e865503460f94b8a1d3/html5/thumbnails/8.jpg)
Solve:
Solution:Two Isosceles
Triangles1.90- 28 = 622.180-62-62 = 563.X=56
![Page 9: Objectives: Use properties of isosceles and equilateral triangles Use properties of right triangles](https://reader036.vdocuments.us/reader036/viewer/2022082611/56649e865503460f94b8a1d3/html5/thumbnails/9.jpg)
Solve:
Solution:Two Isosceles
Triangles1.180 – 65-65 = 502.180 – 50-50 = 803.X= 80
65
50
50
50=80
![Page 10: Objectives: Use properties of isosceles and equilateral triangles Use properties of right triangles](https://reader036.vdocuments.us/reader036/viewer/2022082611/56649e865503460f94b8a1d3/html5/thumbnails/10.jpg)
Solve:
Solution:1.120 = 60+602.60= 60 vertical
angles3.X = 60
60
60
60
60
60
![Page 11: Objectives: Use properties of isosceles and equilateral triangles Use properties of right triangles](https://reader036.vdocuments.us/reader036/viewer/2022082611/56649e865503460f94b8a1d3/html5/thumbnails/11.jpg)
Try this one:
Solution:12 = 2x -1224 = 2xX = 12
![Page 12: Objectives: Use properties of isosceles and equilateral triangles Use properties of right triangles](https://reader036.vdocuments.us/reader036/viewer/2022082611/56649e865503460f94b8a1d3/html5/thumbnails/12.jpg)
One More:
Solution:1.180-68-68 = 442.90 - 44 = 463.4x – 2 = 46Solve for x4x = 48X = 12
44
68
![Page 13: Objectives: Use properties of isosceles and equilateral triangles Use properties of right triangles](https://reader036.vdocuments.us/reader036/viewer/2022082611/56649e865503460f94b8a1d3/html5/thumbnails/13.jpg)
Last One:
Solution:1.146 = 13x + 32.143 = 13x3.11