Given: △ABC where CB =a, AC=b, and AB=c and a2 +b2 =c2

Question

Construct: Right △DEF such that AC¯¯¯¯¯¯¯¯≅FD¯¯¯¯¯¯¯¯ and CB¯¯¯¯¯¯¯¯ ≅ DE¯¯¯¯¯¯¯¯
Prove: △ABC is a right triangle

Read the statements of proof. Then, answer the question.

Statements Reasons
1. △ABC where CB =a, AC=b, and AB=c and a2 +b2 =c2 1. Given
2. Construct right △DEF such that AC¯¯¯¯¯¯¯¯≅FD¯¯¯¯¯¯¯¯ and CB¯¯¯¯¯¯¯¯ ≅ DE¯¯¯¯¯¯¯¯ 2. Construction
3. (AB)2 = (AC)2 + (CB)2 3. Substitution Property
4. 4. Pythagorean Theorem
5. AC=FD

CB=DE

5. Definition of congruence
6. (EF)2 = (AC)2 + (CB)2 6.
7. (EF)2 = (AB)2 7. Transitive Property
8. 8. Calculations (square root)
9. EF¯¯¯¯¯¯¯¯ ≅ AB¯¯¯¯¯¯¯¯ 9. Definition of congruence
10. △ABC ≅ △FED 10. SSS
11. ∠C ≅ ∠D 11. CPCTC
12. m∠C = m∠D 12. Definition of congruence
13. m∠D = 90° 13.
14. m∠C = 90° 14.
15. △ABC is a right triangle 15. Definition of right triangles


What reason justifies statement 13?

(1 point)
Responses

Transitive Property
Transitive Property

Definition of right triangles

Answer 1

The reason that justifies statement 13 is:

Definition of right triangles

This is because statement 13 asserts that angle \( D \) is a right angle, and it follows from the properties of the right triangle \( DEF \) that was constructed as part of the proof.