Question

5 practice 5 (from unit 2, lesson 12)
priya is convinced the diagonals of the isosceles trapezoid are congruent. she knows that if she can prove triangles congruent that include the diagonals, then she will show that diagonals are also congruent.
help her complete the proof.
abde is an isosceles trapezoid.
\\( \overline { a e } \cong \overline { b d } \\)
\\( \angle a \cong \angle b \\)
\\( \angle e \cong \angle d \\)
drag and drop the correct choices into the boxes to complete the proof.
draw auxiliary lines that are diagonals and ab is congruent
to because they are the same segment. we know angle b and
are congruent. we know ae is congruent to. therefore, triangle abe and
are congruent because of. finally, diagonal be is congruent to
\\( a e \\) because.

Explanation:

Explicación breve:

Para demostrar que las diagonales de un trapecio isósceles son congruentes, se dibujan las diagonales \( BE \) y \( AD \). \( AB \) es congruente a sí mismo (segmento común). En un trapecio isósceles \( \angle A\cong\angle B \) y \( AE\cong BD \) (dado). Usando el teorema de congruencia de triángulos L - A - L (Side - Angle - Side), los triángulos \( ABE \) y \( BAD \) son congruentes. Finalmente, las diagonales \( BE \) y \( AD \) son congruentes porque las partes correspondientes de triángulos congruentes son congruentes (CPCTC).

Respuesta:

1. \( BE \)
2. \( AD \)
3. \( AB \)
4. \( \angle A \)
5. \( BD \)
6. \( \triangle BAD \)
7. Side - Angle - Side Triangle Congruence Theorem
8. \( AD \)
9. Corresponding parts of congruent figures are congruent

Answer:

Explicación breve:

Para demostrar que las diagonales de un trapecio isósceles son congruentes, se dibujan las diagonales \( BE \) y \( AD \). \( AB \) es congruente a sí mismo (segmento común). En un trapecio isósceles \( \angle A\cong\angle B \) y \( AE\cong BD \) (dado). Usando el teorema de congruencia de triángulos L - A - L (Side - Angle - Side), los triángulos \( ABE \) y \( BAD \) son congruentes. Finalmente, las diagonales \( BE \) y \( AD \) son congruentes porque las partes correspondientes de triángulos congruentes son congruentes (CPCTC).

Respuesta:

1. \( BE \)
2. \( AD \)
3. \( AB \)
4. \( \angle A \)
5. \( BD \)
6. \( \triangle BAD \)
7. Side - Angle - Side Triangle Congruence Theorem
8. \( AD \)
9. Corresponding parts of congruent figures are congruent