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3 - 5 Midline Theorem

The document describes an isosceles triangle ABC with base AC and midline DE. It asks the reader to find several values related to the sides and angles of the triangle, including: proving triangles ADB and CDB are right triangles, finding the value of x if AC = x - 10 and DE = 6, and determining the measure of several angles of the triangle. The document uses a two-column format to prove triangles ADB and CDB are right triangles and provides information about the midline of a triangle being parallel to the third side.

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NeWo YanTot
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1K views14 pages

3 - 5 Midline Theorem

The document describes an isosceles triangle ABC with base AC and midline DE. It asks the reader to find several values related to the sides and angles of the triangle, including: proving triangles ADB and CDB are right triangles, finding the value of x if AC = x - 10 and DE = 6, and determining the measure of several angles of the triangle. The document uses a two-column format to prove triangles ADB and CDB are right triangles and provides information about the midline of a triangle being parallel to the third side.

Uploaded by

NeWo YanTot
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PPT, PDF, TXT or read online on Scribd
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In the given triangle, find the

value of x, and the m<ABC.


In the figure shown below, segment BD bisects
segment AC, and segment AB is congruent to
segment BC.

 Prove that triangle ADB and triangle CDB


are right triangles. Use a two-column
proof.
What can you  The area of the triangle is
conclude about the equal to the area of the
area of the two
shapes? parallelogram.

Area of triangle Area = ½ (B x H)

Area of Area = B x H
parallelogram
The segment joining the midpoints of two
Midline
sides of a triangle is parallel to the third
Theorem
side and is half as long as the third side.
Example 1:

Find the
value of x.
B is the midpoint of segment AC, D is the
Example 2: midpoint of segment CE, and AE = 17.
Find BD.
a. If AC = 10 and AB = 16, find
ABC is an AD, BE, and DE.
isosceles
triangle b. If AC = x - 10 and DE = 6, find
with base the value of x.
AC and
midline DE.
Find the
value of x,
y, and z.
D is the midpoint of segment AC, E is the
midpoint of segment AB.

x = ___ AB = ___
y = ___ AC = ____
z = ___ CB = ____
m ABC = _____ m DEB = _________
m ADE = _______m EDC = _________
m ACB = _______
Write Summary
 At least 3 sentences
1. ABC is an isosceles triangle with B
base and midline
If AC = 10 and AB = 16, find:

AD = _______ BE = ______
DE = _______
D E

2. If AC = x – 10 and DE = 6, find the


value of x.

A C

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