Geometry/Trig
Name: ______________________________
Date: _______________________________
Lesson 4-3 Properties of Triangles
Learning Goals: (7) What are the side angle relationships in a triangle?
Warm Up
1. Given Triangle ABC, A = 2x°, B = x+5°, C = 3x+7°
a. find the measurement of angle B.
b. Is triangle ABC acute, obtuse, or right? Justify your answer.
Labeling Triangles
Rules for labeling Triangles:
Sides of triangles are always labeled as __________________ letters.
Angles of triangles are always labeled as __________________ letters
The same letters are always ACROSS from each other!!!
Let’s Try This!
1. Given triangle ABC, a = 25cm, =74°, c = 15cm, , , and b = 18cm. Draw and label
the triangle below.
Use your notes
from 2-2 guide
your thinking,
and refresh your
memory!
Geometry/Trig
Angle-Side Relationships in Triangle:
Consider ABC as shown below with given
side lengths and angle measures:
Turn and Talk: With your elbow partner, answer the three questions below 1) List the angles (by name) in order from smallest to biggest:
2) List the sides (by name) of the triangle in order from smallest to biggest:
3) Write a conjecture that describes a relationship between the measure of angles and the measure of sides:
BE PREPARED TO SHARE OUT!
Side-Angle Relationships:
The ______________ side is across from the ______________ angle.
The ______________ side is across from the ______________ angle.
The ______________ side is across from the ______________ angle.
Geometry/Trig
Let’s Try It!
1. In ABC, A = 30° and B = 50°. Name the longest side of the triangle, and explain how you
know.
2. In triangle ABC, A = 36°, and C = 110°. Write the order of the sides of this triangle in order from
least to greatest?
3. You are constructing a stage prop that shows a large triangular mountain. The bottom edge of the
mountain is about 32 feet long, the left slope is about 24 feet long, and the right slope is about 26 feet long.
a) List the angles of △JKL in order from smallest to largest.
b) How were you able to tell which angle was the smallest?’
Geometry/Trig Angle – Side Relationship Partner Playtime
Choose who will be partner peanut butter and who will be partner jelly. Work on your column’s questions. Each
problem is different, but your multiple choice answers should match. If there is a discrepancy between answers,
figure out who is right and help your partner correct their mistake. Work on both #3 questions together.
Partner Peanut Butter Partner Jelly
1
In ABC, AB=7, BC=12, AC=9. Which list has the
angles of ABC in order from smallest to largest
a. A, B, C
b. B, A, C
c. C, B, A
d. C, A, B
In ABC, AB=25, BC=30, AC=15. Which list has
the angles of ABC in order from largest to smallest
a. B, A, C
b. C, B, A
c. A, C, B
d. C, A, B
2
Given ABC, and B = 45° = 55°. What is
the order of the sides in length, from longest to
shortest?
1) , ,
2) , ,
3) , ,
4) , ,
In ABC, = 65° and B = 70°. What is the
order of side lengths from shortest to longest are
1) , ,
2) , ,
3) , ,
4) , ,
Geometry/Trig
Together
3
In PQR, PQ = 8, QR = 12, and RP = 13. Which
statement about the angles of PQR must be true?
a. Q P R
b. Q R P
c. R P Q
d. P Q
In MTR, MR = 31, TR = 40, and MT = 23. Which
statement about the angles of MTR must be true?
a. R T M
b. T R M
c. M T R
d. T M R
Practice:
1. In , , , and . What is the smallest angle? Justify your answer.
2. Determine which side of the given triangle is the longest. Justify your answer.
What type of triangle is the triangle above according to its angles? Justify your response.
Geometry/Trig
Name: ______________________________
Date: _______________________________
Lesson 4-3: Homework
1. In , , and . Which expression correctly relates the lengths of the
sides of this triangle?
2. Determine and state the largest angle of , and justify how you obtained your answer.
3. In the diagram below of with side extended through D, and .
a. What is the measurement of ?
b. Which side of is the longest side? Justify your answer.
1) 2) 3) 4)
Geometry/Trig 4. In △ABC, m A = 95, m B = 50, and m C = 35.
a. What is the smallest side?
b. Explain how you know.
5. In ABC, m A = x° and m B = 2x+2° and m C = 3x+4°.
a. Find the measurement of A
b. Find the measurement of B
c. Find the measurement of C
d. Classify this triangle according to its angles. Justify your answer.
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