Download Name:___________________________________ Date:__________ Period:_______

Name:___________________________________
Date:__________
Chapter 6: Similar Triangles
Topic 3: Midsegment in Triangles
Period:_______
Do Now:
You will need a compass and a straightedge.
1.) We are going to construct a midsegment of a triangle.
(a) Given triangle ABC, construct the midpoints of AB and AC and label them
as X and Y respectively.
(b) Draw midsegment XY.
(1) Compare <AXY to <ABC and compare <AYX to <ACB. Without using a protractor what would guess the
relationship between these two pairs of angles is?
(2) What does that imply about the relationship between XY and BC?
Vocabulary:
A _____________________________ of a triangle is formed by connecting the
_____________________________ of two sides of a triangle.
The _____________________________ of a triangle is _____________________________ to the third side of
the triangle and it is _____________________ the length of the third side.
DE is the midsegment of
if
________________________________
________________________________
Examples:
Apply what you know about the properties of midsegments to solve the following questions.
1.) Using the diagram below of
2.) QR is a midsegment in
?
, find the value of x and the perimeter of quadrilateral MAHB.
, QR = 14, BQ = 11, and CR = 9. What is the length of AC and the perimeter of
3.) SP is a midsegment of
. Use the diagram below to answer the following questions.
(a) What is the measure of <GPS?
(b) What is the measure of <DSP?
4.) MT is a midsegment of
. Use the diagram below to answer the following questions.
(a) What is the measure of <O?
(b) What is the measure of <E?
(c) What is the measure of <TMO?
5.) CA, AT, and TC are midsegments in ∆DOG. If CA = 8, CT = 10, and AT = 5, what is the perimeter of ∆DOG?
6.) ST, TU, and SU are midsegments in ∆QRS. If CP = 11, QR = 15, and PR = 20, what is the perimeter of ∆STU?
Name:___________________________________
Midsegment in Triangles: Homework
Date:__________
Period:_______
Complete all of the questions below.
1.) In the diagram below of
,
the perimeter of quadrilateral FDEC.
and
are midsegments. If DE = 9, and BC = 17, determine and state
2.) In
shown below, L is the midpoint of
, M is the midpoint of
= 8, ML = 5, and NL = 6, the perimeter of trapezoid BMNC is
(1) 35
, and N is the midpoint of
. If MN
(2) 31
(3) 28
(4) 26
3.) In the diagram of
below, A is the midpoint of
, B is the midpoint of
, C is the midpoint of
and
and
are drawn. If VW = 7x – 3 and AB = 3x + 1, what is the length of ?
,
4.) In the diagram below,
is a midsegment in triangle WXY. Use the diagram to below to find the measure of
<WSR and <XRS. What is the length of ?
Review Questions:
5.) Quadrilateral MATH has coordinates M(-6,-3), A(-1,-3), T(-2,-1), and H(-4,-1). The image of quadrilateral
MATH after composition
is quadrilateral M”A”T”H”. State and label the coordinates of M”A”T”H”.
6.) When writing a geometric proof, which angle relationship could be used alone to justify that two angles are
congruent?
(1) supplementary angles
(2) adjacent angles
(3) linear pair of angles
(4) vertical angles
7.) The two lines represented by the equations below are graphed in a coordinate plane.
x + 6y = 12
3(x – 2) = -y – 4
Which statement best described the two lines?
(1) The lines are parallel.
(2) The lines are the same line.
(3) The lines are perpendicular.
(4) The lines intersect at an angle other than 90o.