Question

Drag each justification to the correct step to complete the proof. Not all justifications will be used. Given: , A is the midpoint of , and B is the midpoint of. Prove: The geometry of scalene triangle XYZ with base YZ, and legs XY and XZ. The legs are divided by a line AB. AB is parallel to the base. Symmetric property. Corresponding angles are congruent in congruent triangles. SSS congruency. Definition of a midpoint. Reflexive property.

Answer 1

To prove that triangle XYZ is a scalene triangle with base YZ and legs XY and XZ, we can use the given information of midpoints and parallel lines, as well as congruency to triangle ABX.

Step-by-step explanation:

To prove that triangle XYZ is a scalene triangle with base YZ and legs XY and XZ, we can use the following steps:

Given that A is the midpoint of XY and B is the midpoint of XZ, we know that AB is parallel to YZ because corresponding angles in congruent triangles are congruent.

Since AB is parallel to YZ, we can use the SSS congruency (Side-Side-Side) to prove that triangle XYZ is congruent to triangle ABX.

Using the definition of a midpoint, we know that AB = BX.

Therefore, triangle XYZ is a scalene triangle with base YZ and legs XY and XZ.

Answer 2

To prove that triangle XYZ is a scalene triangle with base YZ and legs XY and XZ, we can use the given information of midpoint A and B. By establishing that AB is parallel to YZ, we can show that all three sides of XYZ are of different lengths.

Step-by-step explanation:

To prove that triangle XYZ is a scalene triangle with base YZ and legs XY and XZ, we can use the given information:

1. A is the midpoint of XY

2. B is the midpoint of XZ

To prove that the triangle is scalene, we need to show that all three sides are of different lengths. Here's a step-by-step proof:

Step 1: Given that A is the midpoint of XY and B is the midpoint of XZ, we know that AB is parallel to YZ according to the definition of a midpoint.

Step 2: Using the symmetric property, we can show that YZ is parallel to AB.

Step 3: Since AB is parallel to YZ, we can conclude that the corresponding angles of the triangles XYZ and XAB are congruent.

Step 4: Finally, using the SSS congruency, we can prove that the triangles XYZ and XAB are congruent, which means that all three sides of triangle XYZ are of different lengths, making it a scalene triangle.