Geometry/Trig

Name: ______________________________

Date: _______________________________

Lesson 2-3 Properties of Triangles

Learning Goals: (7) What are the side angle relationships in a triangle?

Warm Up

1. 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.

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, ∠𝐵=74°, c = 15cm, ∠𝐶 = 20°,∠𝐴 = 86°, 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 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?’

Geometry/Trig

Partner - Practice: 1. In , , , and . What is the smallest angle? Justify your answer.

2. a) Determine which side of the given triangle is the longest. Justify your answer.

b) What type of triangle is the triangle above according to its angles? Justify your response.

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 ΔABC, AB=7, BC=12, AC=9. Which list has the

angles of ΔABC in order from smallest to largest

a. ∠A, ∠B, ∠C

b. ∠B, ∠A, ∠C

c. ∠C, ∠B, ∠A

d. ∠C, ∠A, ∠B

In ΔABC, AB=25, BC=30, AC=15. Which list has

the angles of ΔABC in order from largest to smallest

a. ∠B, ∠A, ∠C

b. ∠C, ∠B, ∠A

c. ∠A, ∠C, ∠B

d. ∠C, ∠A, ∠B

Geometry/Trig

2

Given ∆ABC, and 𝑚∡B = 45° 𝑚∡𝐶 = 55°. What is

the order of the sides in length, from longest to

shortest?

1) , ,

2) , ,

3) , ,

4) , ,

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) , ,

Together

3

In ∆PQR, PQ = 8, QR = 12, and RP = 13. Which

statement about the angles of ∆PQR must be true?

a. 𝑚∠Q > 𝑚∠P > 𝑚∠R

b. 𝑚∠Q > 𝑚∠R > 𝑚∠P

c. 𝑚∠R > 𝑚∠P > 𝑚∠Q

d. 𝑚∠P > 𝑚∠𝑅 > 𝑚∠Q

In ∆MTR, MR = 31, TR = 40, and MT = 23. Which

statement about the angles of ∆MTR must be true?

a. 𝑚∠R < 𝑚∠T < 𝑚∠M

b. 𝑚∠T < 𝑚∠R < 𝑚∠M

c. 𝑚∠M < 𝑚∠T < 𝑚∠R

d. 𝑚∠T < 𝑚∠M < 𝑚∠R

Geometry/Trig

Name: ______________________________

Date: _______________________________

Lesson 2-3: Homework

1. Determine and state the largest angle of ∆𝑅𝑆𝑇, and justify how you obtained your answer.

2. In the diagram below of with side extended through D, and

.

a. What is the measurement of ∡𝐵?

b. Calculate the measurement of ∡𝐵𝐶𝐴?

c. Which side of is the longest side? Justify your answer.

3. In △ABC, m∠A = 95, m∠B = 50, and m∠C = 35.

a. What is the smallest side?

b. Explain how you know.

Geometry/Trig

4. 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.

5. In , , and . Which expression correctly relates the lengths of the sides of this

triangle?

1)

2)

3)

4)