Hinge Theorem - Practice

Front

What is the Hinge Theorem?

Back

The Hinge Theorem states that if two triangles have two sides of equal length and the included angle of one triangle is larger than the included angle of the other, then the side opposite the larger angle is longer.

Front

If two triangles have two equal sides, how can you determine which triangle has the longer third side?

Back

You can determine which triangle has the longer third side by comparing the measures of the included angles. The triangle with the larger included angle will have the longer third side.

Front

In triangle ABC, if AB = AC and angle B is larger than angle C, which side is longer?

Back

Side AC is longer than side AB because angle B is larger than angle C.

Front

If two sides of a triangle are equal, what can be said about the angles opposite those sides?

Back

The angles opposite the equal sides are also equal, according to the Isosceles Triangle Theorem.

Front

In triangle DEF, if DE = DF and angle E is larger than angle F, which side is longer?

Back

Side EF is longer than side DE because angle E is larger than angle F.

Front

What is the relationship between angles and sides in a triangle?

Back

In a triangle, the larger the angle, the longer the side opposite that angle.

Front

If triangle GHI has GH = GI and angle H is the largest angle, which side is the longest?

Back

Side HI is the longest side because it is opposite the largest angle H.

Front

How can you use the Hinge Theorem to compare two triangles?

Back

You can use the Hinge Theorem by checking the lengths of two sides and the measures of the included angles to determine which triangle has the longer opposite side.

Front

In triangle JKL, if JK = JL and angle K is smaller than angle L, which side is shorter?

Back

Side KL is shorter than side JK because angle K is smaller than angle L.

Front

What does it mean if two triangles are congruent?

Back

Two triangles are congruent if they have the same size and shape, meaning all corresponding sides and angles are equal.