- By
**keran** - Follow User

- 105 Views
- Uploaded on

Download Presentation
## PowerPoint Slideshow about ' Concept' - keran

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

BCA is opposite BA and A is opposite BC, so BCA A.

___

Congruent Segments and Angles

A. Name two unmarked congruent angles.

Answer: BCAand A

Example 1BC is opposite D and BD is opposite BCD, so BC BD.

___

___

___

___

Answer: BC BD

Congruent Segments and Angles

B. Name two unmarked congruent segments.

Example 1A. Which statement correctly names two congruent angles?

A.PJM PMJ

B.JMK JKM

C.KJP JKP

D.PML PLK

Example 1aA.JP PL

B.PM PJ

C.JK MK

D.PM PK

B. Which statement correctly names two congruent segments?

Example 1bSince QP = QR, QP QR. By the Isosceles Triangle Theorem, base angles P and R are congruent, so mP = mR . Use the Triangle Sum Theorem to write and solve an equation to find mR.

Find Missing Measures

A. Find mR.

Triangle Sum Theorem

mQ = 60, mP = mR

Simplify.

Subtract 60 from each side.

Answer:mR = 60

Divide each side by 2.

Example 2B. Find PR.

Since all three angles measure 60, the triangle is equiangular. Because an equiangular triangle is also equilateral, QP = QR = PR. Since QP = 5, PR = 5 by substitution.

Answer:PR = 5 cm

Example 2Since E = F, DE FE by the Converse of the Isosceles Triangle Theorem. DF FE, so all of the sides of the triangle are congruent. The triangle is equilateral. Each angle of an equilateral triangle measures 60°.

Find Missing Values

ALGEBRA Find the value of each variable.

Example 3mDFE = 60 Definition of equilateral triangle

4x – 8 = 60 Substitution

4x = 68 Add 8 to each side.

x = 17 Divide each side by 4.

The triangle is equilateral, so all the sides are congruent, and the lengths of all of the sides are equal.

DF = FE Definition of equilateral triangle

6y + 3 = 8y – 5 Substitution

3 = 2y – 5 Subtract 6y from each side.

8 = 2y Add 5 to each side.

Example 3Find the value of each variable.

A.x = 20, y = 8

B.x = 20, y = 7

C.x = 30, y = 8

D.x = 30, y = 7

Example 3
Download Presentation

Connecting to Server..