Download Lesson 29: Special Lines in Triangles

GEOMETRY
Lesson 29
NYS COMMON CORE MATHEMATICS CURRICULUM
Name________________________________________
M1
Date_________________________
Lesson 29: Special Lines in Triangles
A mid segment of a triangle is a segment
whose endpoints are midpoints of two sides of the triangle.
Given: BD AE
CBD and CAE are corresponding angles, which are congruent.
CDB and CEA are corresponding angles, which are congruent.
Exercises 1–5
Apply what you know about the properties of mid segments to solve the following examples.
1. 𝑥 =
2. 𝑥 =
𝑦=
Perimeter of △ 𝐴𝐵𝐶 =
Perimeter of Trapezoid DEBC ______
D
E
Lesson 29:
Date:
Special Lines in Triangles
12/14/15
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3. G is the midpoint of segment AC.
H is the midpoint of segment AB.
I is the midpoint of segment BC.
Find x.
𝑥=
4.
If 𝐺𝐻, 𝐻𝐼, 𝐺𝐼 are mid-segments of ∆ABC, find the perimeter of ∆ABC.
8
4
5.
7
If 𝐴𝐵 is a mid-segment of ∆XYZ, find x.
2x + 8
3x + 24
Lesson 29:
Date:
Special Lines in Triangles
12/14/15
© 2014 Common Core, Inc. Some rights reserved. commoncore.org
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This work is licensed under a
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Name:______________________________
Date________________
Geometry M1L29 Special Lines in a Triangle-Mid segment HW Period_____________
̅̅̅̅ is a mid-segment of △ 𝑪𝑾𝑿. 𝑩𝑿 = 𝑨𝑾.
1. ̅̅̅̅̅
𝑾𝑿 is a mid-segment of △ 𝑨𝑩𝑪, and 𝒀𝒁
a. Is CX = CW? Why or why not?
b. If the measure of YZ = 2, what is the measure of WX?
c. What is the measure of AB?
2. If 𝐴𝐵 is a mid-segment of ∆XYZ, find x.
4.
3.
According to the diagram, is a 𝐷𝐸
mid-segment of ∆ABC? Justify your
answer.
If 𝐷𝐸, 𝐸𝐹, 𝐷𝐹 are mid-segments of ∆ABC, find the perimeter of ∆ABC.
Lesson 29:
Date:
Special Lines in Triangles
12/14/15
© 2014 Common Core, Inc. Some rights reserved. commoncore.org
S.160
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
5.
Find the length of the mid-segment.
Challenge Question!!!
𝑊 , 𝑋, 𝑌, and 𝑍 are the midpoints of
̅̅̅̅
𝐴𝐷, ̅̅̅̅
𝐴𝐵 ,̅̅̅̅̅
𝐵𝐶 , and ̅̅̅̅
𝐶𝐷 respectively.
𝐴𝐷 = 18, 𝑊𝑍 = 11, and 𝐵𝑋 = 5.
m∠𝑊𝐴𝐶 = 33°, m∠𝑅𝑌𝑋 = 74°.
a. ∠𝐷𝑍𝑊 =
b. Perimeter of 𝐴𝐵𝑌𝑊 =
c. Perimeter of 𝐴𝐵𝐶𝐷 =
d. m∠𝑊𝐴𝑋 =
m∠𝐵 =
m∠𝑌𝐶𝑍 =
m∠𝐷 =
e. What kind of quadrilateral is 𝐴𝐵𝐶𝐷?
Lesson 29:
Date:
Special Lines in Triangles
12/14/15
© 2014 Common Core, Inc. Some rights reserved. commoncore.org
S.161
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.