Download Sec 2 Honors Notes 3.1, 3.2 (Carnegie) 3.1: Pg 212 Triangle Sum

Sec 2 Honors Notes 3.1, 3.2 (Carnegie)
3.1: Pg 212 Triangle Sum Activity: The teacher has a large colored triangle on the board. A student is going to tear
off each corner of the triangle to make a discovery about the sum of the angles in a triangle. Write a sentence
describing the discovery made in the activity:
The Triangle Sum Theorem says:
1.
a.
b.
c.
d.
e.
f.
Write a description for each of the following triangles:
Acute:
Obtuse:
Right:
Scalene:
Isosceles:
Equilateral:
2. Pg 213 Use a straight edge to draw a large scalene triangle in the space below. Label the sides of the
triangle S, M and L for small, medium and large. Use a protractor to measure and record the size of each
interior angle of the triangle and label the angles S, M and L. Compare your results with your partner and
the class.
What conclusion can we draw about the relationship between the lengths of the sides of a triangle and the
measure of the interior angles?
3. Pg 217 List the sides from shortest to longest. Complete the problems below, then compare with your
partner.
Pg 219 The remote interior angles of a triangle are the two angles that are non-adjacent to the specified angle.
4. Pg 220. Prove the Exterior Angle Theorem. Work with the partner. Be prepared to explain your reasoning
to the class.
The Exterior Angle Theorem says: The measure of the exterior angle of a triangle is equal to the sum of the
measures of the two remote interior angles of the triangle.
Given: Triangle ABC with exterior angle ∠𝐴𝐶𝐷
Prove: 𝑚∠𝐴 + 𝑚∠𝐵 = 𝑚∠𝐴𝐶𝐷
STATEMENTS
REASONS
2. triangle sum theorem
3. linear pairs are supplementary
5.Subtraction property
5. Pg 221 #14 Solve for x and give the angle measures. Complete problem b if you have time complete d.
6. The Exterior Angle Inequality Theorem says: an exterior angle must be larger than either remote interior
angles. Use the diagram below to discuss this theorem as a class:
3.2. Pg 230 Pasta Activity Sarah thinks any three lengths can represent the lengths of the sides of a triangle.
Sam does not agree. Let’s explore. Take your piece of pasta and break it a two random points so the strand is
divided into three pieces. Measure each of your three pieces in centimeters to the tenths place. Try to form a
triangle from your three pieces of pasta. List your three lengths below and state whether or not the lengths could
form a triangle.
__________________________________________________________________________________________
Random sample of class measurements:
Piece 1 (cm)
Piece 2 (cm)
Piece 3 (cm)
Forms a triangle? (yes/no)
7. With your partner write a hypothesis for what must be true for the 3 lengths to be able to form a triangle.
Be prepared to share your statement with the class.
Is it possible to form a triangle using segments with the following measurements? Sketch a diagram and explain
your answers.
a. 1.9 cm, 5.2 cm, 2.9 cm
b. 152 cm, 73 cm, 79 cm
Pg 233: 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.
Compare this statement with the statement you wrote in #7 above.