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Use the information to complete the proof.

Information
In triangle A B C, segment C D is an altitude and segment A D is congruent to segment B D.

Triangle A B C.Short description, Triangle A B C.,Long description,
Triangle A B C is divided into 2 right triangles by altitude C D. The resulting 2 right triangles are triangle A D C and triangle B D C, with the right angles at angle A D C and angle B D C.

Question
Move options into the table to complete the proof that triangle A B C is an isosceles triangle.

Response area with 7 blank spaces
Statement Reason
segment A D is congruent to segment B D

Given

angle A D C is congruent to angle B D C

Right angles are congruent.

Blank space 22 empty
is congruent to
Blank space 23 empty

Blank space 24 empty

triangle A D C is congruent to triangle B D C

Side-Angle-Side congruence

Blank space 25 empty
is congruent to
Blank space 26 empty

Blank space 27 empty

triangle A B C is an isosceles triangle.

Blank space 28 empty


Answer options with 8 options.

1 answer

Here is how you can complete the proof using the provided information:

| Statement | Reason | |-----------------------------------------------------|-------------------------------------------| | segment A D is congruent to segment B D | Given | | angle A D C is congruent to angle B D C | Right angles are congruent. | | segment C D is congruent to segment C D | Reflexive property. | | segment A C is congruent to segment B C | Corresponding parts of congruent triangles. | | triangle A D C is congruent to triangle B D C | Side-Angle-Side congruence. | | angle A B C is congruent to angle B A C | Corresponding angles of isosceles triangles. | | triangle A B C is an isosceles triangle | Definition of an isosceles triangle. |

You can fill out the blanks as follows:

  • Blank space 22: segment C D is congruent to segment C D
  • Blank space 23: segment A C
  • Blank space 24: segment B C
  • Blank space 25: segment A C
  • Blank space 26: segment B C
  • Blank space 27: angle A B C
  • Blank space 28: triangle A B C is an isosceles triangle

This completes the proof.