Download Unit 4 lesson 3 Triangle Theorems


Find the value of x and the measures of the
unknown sides.
R
M
6x - 5
5x
17
2x + 7
L
3x - 4
N
X = 11
LN = MN = 29
S
Q
3x + 10
X=5
QS = RS = QR = 25

Is it possible to form a triangle with the given
lengths? 3, 4, 8
No 3 + 4 = 7 < 8

Determine if three segments that are 7, 14, and 16
units long can form a triangle. If so, classify the
triangle as acute, right, or obtuse.
Yes, the triangle is obtuse

I can recognize triangle theorems

I can discover and apply theorems about triangles
Name a pair of unmarked congruent segments.
___
BC
___ is opposite D and
BD
is opposite
BCD, so
___
___
BC  BD.
Answer: BC  BD
Which statement correctly names two congruent
angles?
A. PJM  PMJ
B. JMK  JKM
A.
B.
C. KJP  JKP
D. PML  PLK
C.
D.
A
B
C
D
ALGEBRA Find the value of each variable.
mDFE = 60
4x – 8 = 60
4x = 68
x = 17
DF = FE
6y + 3 = 8y – 5
3 = 2y – 5
8 = 2y
4 =y
Name two congruent
segments if 1  2.
A.
B.
A.
B.
C.
D.
C.
D.
A
B
C
D

Find the value of x and then
find the measure of both
angles.
mLOW + mOWL = mFLW
x + 32 = 2x – 48
32 = x – 48
80 = x
Answer: So, mFLW = 2(80) – 48 or 112.
and mF0W = 80

Find the measure of each missing angle
m1 = 104
m2 = 76
m 3 = 42
m4 = 48 m5 = 49

Find the measure of each missing angle
m1  50
m2  50
m3  85
m4  45
m5  120

You can list the angles and sides of a triangle from
smallest to largest (or vice versa)
› The smallest side is opposite the smallest angle
› The longest side is opposite the largest angle
List the angles of ΔABC in order from smallest to
largest.
Answer: C, A, B
List the sides of ΔRST in order from
shortest to longest.
A. RS, RT, ST
B. RT, RS, ST
C. ST, RS, RT
D. RS, ST, RT
A.
B.
C.
D.
A
B
C
D

Inequalities in two triangles

Compare how the side lengths and angles are
related

What effect does changing these measures have on
triangles?
Compare the measures AD and BD.
In ΔACD and ΔBCD, AC  BC, CD  CD, and
ACD > BCD.
Answer: By the Hinge Theorem, mACD > mBCD,
so AD > DB.
Compare the measures ABD and BDC.
In ΔABD and ΔBCD, AB  CD,
BD  BD, and AD > BC.
Answer: By the Converse of
the Hinge Theorem,
ABD > BDC.
B. Compare JKM and KML.
A. mJKM > mKML
B. mJKM < mKML
A.
C. mJKM = mKML
D. not enough information
B.
C.
D.
A
B
C
D