Question

Given: angle a, b, d, cong, angle d, c, a, ∠abd≅∠dca, ba ⊥ ad, ad ⊥ dc. Prove: triangle bad≅triangle cda.

Answer 1

To prove that triangle BAD is congruent to triangle CDA, we can use the given information and the properties of right triangles.

Step-by-step explanation:

To prove that triangle BAD is congruent to triangle CDA, we can use the given information and the properties of right triangles. Here is the step-by-step proof:

1. Given: Angle ABD is congruent to angle DCA. BA is perpendicular to AD. AD is perpendicular to DC.
2. By definition, if two angles of a triangle are congruent to two angles of another triangle, then the third angle of the first triangle will be congruent to the third angle of the second triangle.
3. Since angle ABD is congruent to angle DCA, it follows that angle BAD is congruent to angle CDA.
4. By definition of perpendicular lines, if two lines are perpendicular to the same line, then they are parallel to each other.
5. Since BA is perpendicular to AD and AD is perpendicular to DC, BA is parallel to DC.
6. Using the properties of right triangles, BA is congruent to CD because they are opposite sides of the right angles.
7. By the Side-Angle-Side congruence postulate, triangle BAD is congruent to triangle CDA.