Download Secondary 2 Chapter 3/4 1 3.1/3.2 – Triangle Sum, Exterior Angle

Secondary 2
Chapter 3/4
3.1/3.2 – Triangle Sum, Exterior Angle, Exterior Angle Inequality, and Triangle inequality Theorems
The Triangle Sum Theorem states: The sum of the measures of the interior angles of a triangle is 180°.
Example 1: Draw an acute scalene triangle. Use a protractor to measure each interior angle and label the
angles measures.
1. Measure the length of each side of the triangle. Label the sides in your diagram.
2. Which interior angle is opposite the longest side of the triangle?
3. Which interior angle lies opposite the shortest side of the triangle?
Example 2: List the sides from shortest to longest in each diagram.
a.
b.
c.
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Secondary 2
Chapter 3/4
Example 3: Use the diagram shown to answer the following questions.
1. Name the interior angles of the triangle.
2. Name the exterior angles of the triangle.
3. What does 𝑚∠1 + 𝑚∠2 + 𝑚∠3 equal? Explain.
4. What does 𝑚∠3 + 𝑚∠4 equal? Explain.
5. Why does 𝑚∠1 + 𝑚∠2 = 𝑚∠4?
The remote interior angles of a triangle are the two angles that are non-adjacent to the specified exterior
angle.
The Exterior Angle Theorem states: The measure of the exterior angle of a triangle is equal to the sum of the
measures of the two remote interior angles of a triangle.
Example 4: Solve for x in each diagram.
a.
b.
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Chapter 3/4
c.
d.
The Exterior Angle Inequality Theorem states: The measure of the exterior angle of a triangle is greater
than the measure of either of the remote interior angles of the triangle.
Example 4: In groups, roll a dice 3 times to get values for three potential sides of a triangle. Write each of the
three rolls on the chart below. Once you have written them down, using a ruler and the space below,
determine whether the three sides form a triangle.
Roll 1
Roll 2
Roll 3
Forms a triangle?
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Chapter 3/4
1. Compare the lengths that formed a triangle with the ones that did not. What you do notice?
2. Under what conditions were you able to form a triangle?
3. Under what conditions were you unable to form a triangle?
Example 5: Determine if it is possible to form a triangle using segments with the following measurements.
Explain your reasoning.
a. 2 cm, 5.1 cm, 2.4 cm
b. 9.2 cm, 7 cm, 1.9 cm
The Triangle Inequality Theorem states: The sum of the lengths of any two sides of a triangle is greater than
the length of the third side.
Example 6: Determine the types of triangles based on side measures.
If 𝑎2 + 𝑏 2 = 𝑐 2 , it is a right triangle.
If 𝑎2 + 𝑏 2 > 𝑐 2 , it is an acute triangle.
If 𝑎2 + 𝑏 2 < 𝑐 2 , it is an obtuse triangle.
a. 12, 5, 13
b. 6, 11,9
c. 8, 10, 12
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Chapter 3/4
Example 7: Write an inequality that expresses the possible lengths of the unknown side of each triangle.
a.
A
b.
D
6 cm
10in
B
C
F
9cm
E
8in
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