Learning Task: Applying Theorems on Triangle Inequalities

Which is always true about the measure of an exterior angle of a triangle?

• It is less than the measure of its adjacent interior angle.

• It is less than the measure of either remote interior angle.

• It is greater than the measure of its adjacent interior angle.

• It is greater than the measure of either remote interior angle.

Which of the following numbers of the same unit could represent the side

lengths of a triangle?

• 1, 3, 5

• 2, 4, 5

• 3, 6, 10

• 4, 5, 11

Which is the largest angle?

• ∠D

• ∠O

• ∠P

• Cannot be determined

Which is the smallest angle?

• ∠D

• ∠O

• ∠P

• Cannot be determined.

Which of the following could be a possible measure of the third side of the

triangle if the two sides measure 12 meters and 25 meters?

• 11 meters

• 13 meters

• 28 meters

• 37 meters

What theorem is applicable in determining the smallest and largest angles of

∆POD?

• Converse of Hinge Theorem or SSS Triangle Inequality Theorem

• Hinge Theorem or SAS Triangle Inequality Theorem

• Triangle Inequality Theorem 2 (Aa→Ss)

• Triangle Inequality Theorem 1 (Ss→Aa)

Which side of ∆SAW is the shortest?

• Cannot be determined

Which side of ∆SAW is the longest?

• Cannot be determined.

What theorem is applicable in determining the shortest and longest sides of

∆SAW?

• Triangle Inequality Theorem 1 (Ss→Aa)

• Triangle Inequality Theorem 2 (Aa→Ss)

• Hinge Theorem or SAS Triangle Inequality Theorem

• Converse of Hinge Theorem or SSS Triangle Inequality Theorem

Given below is ∆ART. List the sides from the longest to the shortest.

• AT̅̅̅̅, AR̅̅̅̅, RT̅̅̅̅

• AR̅̅̅̅, TR̅̅̅̅, TA̅̅̅̅

• RT̅̅̅̅, RA̅̅̅̅, TA̅̅̅̅

• TA̅̅̅̅, TR̅̅̅̅, AR̅̅̅̅