Triangle Proportionality Theorem

If triangle ABC is similar to triangle DEF, and the length of side AB is 6 and side DE is 9, what is the ratio of their corresponding sides?

• 6:9

• 1:2

• 3:4

• 2:5

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

• Their corresponding sides are equal in length.

• Their corresponding sides are in proportion.

• Their corresponding sides are perpendicular to each other.

• Their corresponding sides are congruent.

What similarity shortcut is used when two angles of one triangle are equal to two angles of another triangle?

• SSS (Side-Side-Side) similarity

• SAS (Side-Angle-Side) similarity

• AA (Angle-Angle) similarity

• ASA (Angle-Side-Angle) similarity

If a triangle has sides of lengths 3, 4, and 5, what is the ratio of its sides?

• 3:4:5

• 4:5:6

• 2:3:4

• 5:5:5

What is the significance of the Triangle Proportionality Theorem in solving real-world problems?

• It allows for the determination of unknown lengths and areas in similar figures.

• It provides a method for calculating the angles of triangles.

• It helps in finding the perimeter of any triangle.

• It is used to prove the congruence of triangles.

How do you find the length of a side in a similar triangle?

• Use the Pythagorean theorem to calculate the length.

• Set up a proportion using the lengths of corresponding sides.

• Measure the side directly with a ruler.

• Add the lengths of all sides together.

What does it mean for two triangles to be similar?

• Two triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion.

• Two triangles are similar if they have the same area.

• Two triangles are similar if they are both equilateral.

• Two triangles are similar if one is a right triangle and the other is not.

If a triangle has a height of 12 and a base of 16, what is the area?

• 64 square units

• 80 square units

• 96 square units

• 128 square units

What is the Triangle Proportionality Theorem?

• If a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally.

• The sum of the angles in a triangle is always 180 degrees.

• The area of a triangle is calculated as half the base times the height.

• All sides of an equilateral triangle are equal.

What similarity shortcut is used when two sides of one triangle are proportional to two sides of another triangle and the included angles are equal?

• SAS (Side-Angle-Side) similarity

• SSS (Side-Side-Side) similarity

• AAA (Angle-Angle-Angle) similarity

• ASA (Angle-Side-Angle) similarity