Daily Warm Up Quiz

1
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 ______________________.
• Find the missing measure

x
2
Relationships Within Triangles Midsegments in
Triangles
3
Midsegments of Triangles
At the end of this lesson, you should be able
to use properties of midsegments to solve
problems.
4
Definition Midsegment of a Triangle
is
a segment in a triangle which connects the
midpoints of opposite sides.
A midsegment of a triangle ______________________
________________________________________________
________________
Note A is a midpoint. B is a midpoint. AB is
a midsegment.
5
6
B
A
6
5
5
Midsegment of a Triangle

How many midsegments are there in any triangle?
3

3
4
4
3
5 5
5 5
Three midsegments can be constructed in any
triangle.
6
Triangle Midsegment Theorem

• If a segment in a ? is a midsegment, then it
• is // to the third side
• has length ½ the third side.

7
Identifying Midsegments in Triangles
Identify A, B, or C as a midsegment, then
determine its length.


B 6
C 4.5
5
4
5
3
A
5
A
7
3
5
5
B
C
B
C
4
4
6
6
C 7.5
4
6
7
7
7
A 8
A
A
4
7
8
B
C
6
B
C
8
8
9
7
You can use Triangle Midsegment Theorem to
determine missing measures in triangles.
8
Applying Properties of Midsegments in Triangles
9
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
1. Find the measures of the following a.) ?
ABC b.) ? D c.) ? A d.) ? CBF
A B C
110 70 F E
D
Check Here!
x
10
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?

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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.

x
x _____ y _____
24
64
Homework
26 y
12
Check Your Solution Here
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
PQ ½ ST x 85 ½ (3x 46) 2(x 85) 3x
46 2x 170 3x 46 2x 3x 124 -x -124 x
124
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