answer key for activity 9

1. Activity 9 (answer key)
Materials Needed: ruler, manila paper
Procedures:
1) Replicate the activity table on a piece of a manila paper.
2) Measure using ruler the sides opposite the angles with given sizes. Indicate
the lengths (in mm) on your table.
3) develop the relationship of the angles of a triangle and the lengths of the sides
opposite them by answering the questions below on a piece of manila paper.
Triangle Measures of the
Angle
Length of Sides Opposite the
Angles
ΔZYF
m∠Z 54° FY 14 cm
m∠Y 36° ZF 12 cm
m∠F 90° ZY 17 cm
ΔQUT
m∠Q 81° TU 12 cm
m∠U 61° QT 10 cm

2. m∠T 38° QU 8cm
ΔOMG
m∠O 29° GM 20 cm
m∠M 48° OG 15 cm
m∠G 103° OM 25 cm
1) Is there a relationship between the size and the length of the side
opposite to it?
Yes, there is. No, there isn’t.
2) Making Conjecture: what is the relationship between the angles of a
triangle and the sides opposite them?
 When one angle of triangle is larger than the second angle, the side
opposite the first angle is longer than the side opposite the second
angle.
3) Your findings in no. 2 describe Triangle Inequality Theorem 2. Write it
in if-then form.
If one angle of a triangle is larger than the second angle, then the side
opposite the first angle is longer than the side opposite the second angle.
4) What is the relationship of the largest angle of a triangle and the side
opposite it?
The side opposite to the largest angle of a triangle is also the longest
(in length) side of the triangle.
5) What is the relationship of the smallest angle of a triangle and the side
opposite it?
The side opposite to the smallest angle of a triangle is also the shortest
(in length) side of the triangle.

4. 6) Arrange in increasing order the angles of the triangle in this activity
according to measurement.
Name of
Triangle
Smallest Angle Smaller Angle Largest Angle
ΔZYF ∠Y ∠Z ∠F
ΔQUT ∠T ∠U ∠Q
ΔOMG ∠M ∠O ∠G
7) Arrange in decreasing order the angles of the triangle in this activity
according to their lengths.
Name of
Triangle
Shortest Side Shorter Side Longest Side
ΔZYF FZ/ZF FY/YF YZ/ZY
ΔQUT QU/UQ QT/TQ TU/UT
ΔOMG OG/GO GM/MG OM/MO
8) Having learned Triangle Inequality 2, answer the question in the table.
Kind of Triangle How do you know that a certain
side is the longest?
Acute Δ When the side of a triangle is the
opposite of the largest angle of a
triangle.
Right Δ
Obtuse Δ