Triangle Theorems Flashcard

Front

What is the sum of the interior angles of a triangle?

Back

180°

Answer explanation

The sum of the interior angles of a triangle is always 180°. This is a fundamental property of triangles in Euclidean geometry, making 180° the correct answer.

Tags

CCSS.HSG.CO.C.10

Front

In an isosceles triangle, if one of the base angles measures 40°, what is the measure of the other base angle?

Back

40°

Answer explanation

In an isosceles triangle, the two base angles are equal. Since one base angle measures 40°, the other base angle must also measure 40°. Therefore, the correct answer is 40°.

Tags

CCSS.HSG.CO.C.10

Front

If the segment joining the midpoints of two sides of a triangle is 5 cm, what is the length of the third side of the triangle?

Back

10 cm

Answer explanation

In a triangle, the segment joining the midpoints of two sides is half the length of the third side. Since this segment is 5 cm, the third side must be 10 cm.

Tags

CCSS.HSG.CO.C.10

Front

The medians of a triangle meet at a point called the:

Back

Centroid

Answer explanation

The medians of a triangle intersect at a point called the centroid. This point is the center of mass of the triangle and divides each median into a 2:1 ratio.

Tags

CCSS.HSG.CO.C.10

Front

In a triangle, if two angles measure 45° and 55°, what is the measure of the third angle?

Back

80°

Answer explanation

In a triangle, the sum of the angles is always 180°. Given angles of 45° and 55°, we calculate the third angle as 180° - (45° + 55°) = 180° - 100° = 80°. Thus, the measure of the third angle is 80°.

Tags

CCSS.HSG.CO.C.10

Front

True statement about the base angles of an isosceles triangle.

Back

They are always congruent.

Answer explanation

In an isosceles triangle, the two sides that are equal have base angles that are also equal. Therefore, the correct statement is that the base angles are always congruent.

Tags

CCSS.HSG.CO.C.10

Front

If the segment joining the midpoints of two sides of a triangle is parallel to the third side, what is the relationship between their lengths?

Back

The segment is half the length of the third side.

Answer explanation

In a triangle, the segment joining the midpoints of two sides is known as the midsegment. This midsegment is parallel to the third side and is always half its length, confirming that the correct answer is that the segment is half the length of the third side.

Tags

CCSS.HSG.CO.C.10

Front

In a triangle, if the medians are drawn from each vertex, they will intersect at a point that divides each median in the ratio:

Back

2:1

Answer explanation

In a triangle, the medians intersect at the centroid, which divides each median in the ratio 2:1. This means the segment from the vertex to the centroid is twice as long as the segment from the centroid to the midpoint of the opposite side.

Tags

CCSS.HSG.CO.C.10

Front

If a triangle has angles measuring 60°, 60°, and 60°, what type of triangle is it?

Back

Equilateral

Answer explanation

A triangle with angles measuring 60°, 60°, and 60° has all three angles equal. This means all sides are also equal, making it an equilateral triangle. Therefore, the correct answer is equilateral.

Tags

CCSS.HSG.CO.C.10

Front

Which theorem states that the sum of the measures of the interior angles of a triangle is 180°?

Back

Triangle Sum Theorem

Answer explanation

The Triangle Sum Theorem states that the sum of the measures of the interior angles of a triangle is always 180°. This is a fundamental property of triangles, distinguishing it from other theorems.

Tags

CCSS.HSG.CO.C.10