Download Angle-Side Relationships in Triangle

Geometry/Trig
Name: ______________________________
Date: _______________________________
Lesson 4-2 Properties of Triangles
Learning Goals: (7) What are the side angle relationships in a triangle?
Warm Up
*use your notes to guide your thinking!
1. In ∆𝐸𝐹𝐺, m∠E = 62° and m∠F = 2x° and m∠G = 5x+55°, what is the measure of ∠G.
2. Given Triangle ABC, 𝑚∡A = 2x°, 𝑚∡B = x+5°, 𝑚∡C = 3x+7°
a. find the measurement of angle B.
b. Is triangle ABC acute, obtuse, or right? Justify your answer.
Before we begin: How do we label sides and angles of 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 labeling the triangle below:
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!
Together!
Angle - Side Relationship
The ______________ side is across from the ______________ angle.
The ______________ side is across from the ______________ angle.
The ______________ side is across from the ______________ angle.
Let’s Try It!
Geometry/Trig
1. In Δ ABC, 𝑚∡A = 30° and 𝑚∡B = 50°. Name the longest side of the triangle, and explain how you
know.
2. In triangle ABC, 𝑚∡A = 36°, and 𝑚∡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?’
Angle – Side Relationship Partner Playtime
Geometry/Trig
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
In ΔABC, AB=7, BC=12, AC=9. Which list has the
angles of ΔABC in order from smallest to largest
Partner Jelly
In ΔABC, AB=25, BC=30, AC=15. Which list has
the angles of ΔABC in order from largest to smallest
1
a.
b.
c.
d.
∠A, ∠B, ∠C
∠B, ∠A, ∠C
∠C, ∠B, ∠A
∠C, ∠A, ∠B
a. ∠B, ∠A, ∠C
b. ∠C, ∠B, ∠A
c. ∠A, ∠C, ∠B
d. ∠C, ∠A, ∠B
Given ∆ABC, and 𝑚∡B = 45° 𝑚∡𝐶 = 55°. What is
the order of the sides in length, from longest to
shortest?
In ∆ABC, 𝑚∡𝐴 = 65° and 𝑚∡B = 70°. What is the
order of side lengths from shortest to longest are
1)
2)
3)
4)
1)
2)
3)
4)
2
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
Geometry/Trig
In ∆PQR, PQ = 8, QR = 12, and RP = 13. Which
statement about the angles of ∆PQR must be true?
In ∆MTR, MR = 31, TR = 40, and MT = 23. Which
statement about the angles of ∆MTR must be true?
3
a.
b.
c.
d.
𝑚∠Q >
𝑚∠Q >
𝑚∠R >
𝑚∠P >
𝑚∠P > 𝑚∠R
𝑚∠R > 𝑚∠P
𝑚∠P > 𝑚∠Q
𝑚∠𝑅 > 𝑚∠Q
a.
b.
c.
d.
𝑚∠R < 𝑚∠T < 𝑚∠M
𝑚∠T < 𝑚∠R < 𝑚∠M
𝑚∠M < 𝑚∠T < 𝑚∠R
𝑚∠T < 𝑚∠M < 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.