Question

Drag each description to the correct location to complete the flow chart proof. Given: . D is the midpoint of . . Prove: is an isosceles triangle. A triangle ABC with base AC and legs AB and BC divides into two equal right-angle triangles with the vertical line DB by definition of a midpoint, by CPCTC because all right angles are congruent. Because all right angles are congruent.

Answer 1

To prove that triangle ABC is isosceles, we use the properties of a midpoint and congruent right angles.

Step-by-step explanation:

To prove that triangle ABC is an isosceles triangle, we use the properties of a midpoint and congruent right angles.

1. By definition of a midpoint, D is the point that divides side AC into two equal parts.
2. Since D is the midpoint, AD = DC. This means that AB = AD + DB = DC + DB = CB. Therefore, AB = CB.
3. Additionally, the triangles ABD and CBD are right triangles with congruent right angles at B.
4. By CPCTC (Corresponding Parts of Congruent Triangles are Congruent), we can conclude that the triangles ABD and CBD are congruent.
5. Since the triangles ABD and CBD are congruent, their corresponding sides are congruent. This means that AB = CB.
6. Therefore, triangle ABC is an isosceles triangle with AB = CB.

Answer 2

To prove that triangle ABC is an isosceles triangle, we use the midpoint property and congruence of triangles.

Step-by-step explanation:

The given flowchart proof is about proving that triangle ABC is an isosceles triangle.

First, based on the given information, we know that D is the midpoint of AC, which means AD = DC.

Then, using CPCTC (Corresponding Parts of Congruent Triangles are Congruent), we can conclude that angle ADB = angle CDB.

Since AD = DC and angle ADB = angle CDB, we can conclude that triangle ADB is congruent to triangle CDB by SAS (Side-Angle-Side) congruence.

Therefore, AB = BC, proving that triangle ABC is an isosceles triangle.