Activity 9 (answer key)

Materials Needed: ruler, manila paperProcedures:

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

ΔQUTm∠Q 81° TU 12 cm

m∠U 61° QT 10 cm

What If It’s Larger?

m∠T 38° QU 8cm

ΔOMGm∠O 29° GM 20 cm

m∠M 48° OG 15 cm

m∠G 103° OM 25 cm

QUESTIONS

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.

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 ∠FΔQUT ∠T ∠U ∠QΔOMG ∠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 ΔObtuse Δ