parts of similar triangles, angle bisector

Front

What is a similar triangle?

Back

A triangle that has the same shape as another triangle but may differ in size. The corresponding angles are equal, and the lengths of corresponding sides are proportional.

Front

What is the Angle Bisector Theorem?

Back

The theorem states that the angle bisector of an angle in a triangle divides the opposite side into two segments that are proportional to the lengths of the other two sides.

Front

If two triangles are similar, what can be said about their corresponding angles?

Back

The corresponding angles of similar triangles are equal.

Front

If triangle ABC is similar to triangle DEF, and AB = 4, AC = 6, and DE = 8, what is the length of DF?

Back

DF = 12 (Using the proportionality of sides in similar triangles: AB/DE = AC/DF).

Front

What is the definition of an angle bisector?

Back

An angle bisector is a line or ray that divides an angle into two equal parts.

Front

How do you find the length of the angle bisector in a triangle?

Back

Use the formula: l = (2ab)/(a+b) * cos(C/2), where a and b are the lengths of the sides adjacent to the angle, and C is the angle being bisected.

Front

What is the relationship between the sides of similar triangles?

Back

The lengths of corresponding sides of similar triangles are in proportion.

Front

If triangle XYZ is similar to triangle PQR, and the ratio of their sides is 3:5, what is the ratio of their areas?

Back

The ratio of their areas is 9:25 (the square of the ratio of their corresponding sides).

Front

What is a median in a triangle?

Back

A median is a line segment joining a vertex to the midpoint of the opposite side.

Front

What is a perpendicular bisector?

Back

A perpendicular bisector is a line that divides a line segment into two equal parts at a 90-degree angle.