Daily Warm Up Quiz

1. Define: isosceles triangle 2. Complete each theorem below: If a triangle is isosceles, then __________. If the base angles of a triangle are congruent, then ______________________.3.Find the missing measure:

x

Relationships Within Triangles

Midsegments in Triangles

Midsegments of Triangles

At the end of this lesson, you should be able to

use properties of midsegments to solve problems.

Definition: Midsegment of a Triangle

A midsegment of a triangle ______________________________________________________________________________________

is a

segment in a triangle which connects the midpoints of opposite sides.

5

5

6

6A B

Note: A is a midpoint. B is a midpoint.

AB is a midsegment.

Midsegment of a Triangle

How many midsegments are

there in any triangle?

3

3

4

4

5 5 5 5

3

Three midsegments can be constructed in any triangle.

Triangle Midsegment Theorem

If a segment in a ∆ is a midsegment, then it

is // to the third side has length ½ the third side.

Identifying Midsegments in Triangles

3 3

3

4 4

7

5

A

A

A

A

B C B

BB C

C

C

6 6

5 5

5

4

45

46

6

97

77

8

7

7

8 8

Identify A, B, or C as a midsegment, then determine its length.

B = 6

C = 7.5A = 8

C = 4.5

You can use Triangle Midsegment Theorem to determine missing measures in triangles.

Using Triangle Midsegment Theorem to Find Missing

Measures Q and P are the midpoints of ∆ RST.

What is m RS?...m TQ?....m TS?

R

x + 50

P x + 85

Q

S T

3x + 46

A

B C 110

70

F E D

1. Find the measure of the following:

a.) ∠ ABC

b.) ∠ D

c.) ∠ A

d.) ∠ CBF

70

70

40

110

x

Check Here!

Final Checks: Architecture

The triangular face of the Rock ‘n’ Roll Hall of Fame in Cleveland is isosceles. The length of the base is 229 ft. 6 in. What is the length of the highlighted segment?

Final Checks for Understanding

1. Define midsegment of a triangle.2. Name two properties of

midsegments in triangles.3. Find the missing measures, given a

is a midsegment. a

24

x

64

26 y

x = _____; y = _____

Homework:

Check Your Solution Here:

Click here to return to today’s lesson:

PQ = ½ ST

x + 85 = ½ (3x + 46)

2(x + 85) = 3x + 46

2x + 170 = 3x + 46

2x = 3x – 124

-x = -124

x = 124

PS = x TS = 3x + 46

PS = 124 TS = 3 (124) + 46

RS = RP + PS TS = 372 + 46

RS = 124 + 124 TS = 418

RS= 248

TQ = QR

TQ = x + 50

TQ = 124 + 50

TQ = 174