Section Of Geometry Quiz

1. Which of the following best describes Side Side Side

SSS is used to show that none of the sides of the triangles are the same.

SSS is used to show that all of the sides of the triangles are the same.

SSS is used to show that some of the sides of the triangles are the same.

SSS stands for Side Side Side, which means that all three sides of the triangle are equal in length. This is the definition of an equilateral triangle, where all three sides are the same. Therefore, the correct answer is that SSS is used to show that all of the sides of the triangles are the same.

Explanation

SSS stands for Side Side Side, which means that all three sides of the triangle are equal in length. This is the definition of an equilateral triangle, where all three sides are the same. Therefore, the correct answer is that SSS is used to show that all of the sides of the triangles are the same.

2. ________ ________ ____________ is when 2 triangles have 2 angles that measure the same and a side that is not between them with the same measure.

Angle Angle Side (AAS) is a congruence postulate that states that if two triangles have two angles that are congruent and a side that is not between them that is also congruent, then the triangles are congruent. In other words, if two triangles have two corresponding angles that are equal in measure and a corresponding side that is equal in length, then the triangles are congruent. This postulate can be used to prove that two triangles are congruent and have the same shape and size.

Explanation

Angle Angle Side (AAS) is a congruence postulate that states that if two triangles have two angles that are congruent and a side that is not between them that is also congruent, then the triangles are congruent. In other words, if two triangles have two corresponding angles that are equal in measure and a corresponding side that is equal in length, then the triangles are congruent. This postulate can be used to prove that two triangles are congruent and have the same shape and size.

Submit

3. True or False: When you prove that a triangle is similar to another triangle then you can use that to prove other triangles are similar.

True

False

When you prove that a triangle is similar to another triangle, it means that the corresponding angles of the two triangles are equal and the corresponding sides are proportional. This similarity can be used to prove that other triangles are similar as well. By showing that the corresponding angles of two triangles are equal and the corresponding sides are proportional, you can establish a pattern of similarity that can be applied to other triangles. Therefore, the statement is true.

Explanation

When you prove that a triangle is similar to another triangle, it means that the corresponding angles of the two triangles are equal and the corresponding sides are proportional. This similarity can be used to prove that other triangles are similar as well. By showing that the corresponding angles of two triangles are equal and the corresponding sides are proportional, you can establish a pattern of similarity that can be applied to other triangles. Therefore, the statement is true.

4. True or False: Using ASA is when you have 2 triangles with 2 angles that have the same measure and 1 side NOT included.

True

False

The statement in the question is incorrect. ASA stands for Angle-Side-Angle, which means that you have 2 triangles with 2 angles that have the same measure and the side included between them. In ASA, the side included between the two angles is known, whereas in the statement given in the question, it is mentioned that the side is NOT included. Therefore, the correct answer is False.

Explanation

The statement in the question is incorrect. ASA stands for Angle-Side-Angle, which means that you have 2 triangles with 2 angles that have the same measure and the side included between them. In ASA, the side included between the two angles is known, whereas in the statement given in the question, it is mentioned that the side is NOT included. Therefore, the correct answer is False.

5. There are how many different postulates to prove a triangle? (for both proving a triangle and for similar triangles)

There are seven different postulates to prove a triangle. These postulates are used for both proving a triangle and proving similar triangles.

Explanation

There are seven different postulates to prove a triangle. These postulates are used for both proving a triangle and proving similar triangles.

Submit

6. How do you know if there are similar triangles?

By using the postulates to prove the triangles are similar.

By proving parts of the triangles.

By looking at the triangles.

To determine if there are similar triangles, one can use the postulates to prove that the triangles are similar. This involves comparing the corresponding angles and sides of the triangles to establish if they are proportional. Additionally, one can also prove parts of the triangles to determine if they are similar. This can be done by comparing specific angles or sides of the triangles to see if they are congruent or proportional. Simply looking at the triangles may not provide enough evidence to confirm if they are similar, so relying on postulates and proving parts of the triangles is necessary.

Explanation

To determine if there are similar triangles, one can use the postulates to prove that the triangles are similar. This involves comparing the corresponding angles and sides of the triangles to establish if they are proportional. Additionally, one can also prove parts of the triangles to determine if they are similar. This can be done by comparing specific angles or sides of the triangles to see if they are congruent or proportional. Simply looking at the triangles may not provide enough evidence to confirm if they are similar, so relying on postulates and proving parts of the triangles is necessary.

Submit

7. Side Angle Side is described by which of the following?

2 triangles have 2 sides that have the same length.

A triangle where everything is equal to another triangle.

Side Angle Side (SAS) is described by two triangles having two sides that have the same length, and an angle that measures the same in both triangles and lies between the two sides with the same measure. This is a valid description of the SAS postulate, which states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Explanation

Side Angle Side (SAS) is described by two triangles having two sides that have the same length, and an angle that measures the same in both triangles and lies between the two sides with the same measure. This is a valid description of the SAS postulate, which states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Submit