To prove that AC is congruent to BD in a rectangle, we can use the definitions of a rectangle, the reflexive property, and the triangle congruence postulates.
To prove that AC is congruent to BD, we can use the following steps:
Start by using the definition of a rectangle, which states that all angles are right angles.
Next, apply the reflexive property, which states that any segment is congruent to itself.
Using the Side-Angle-Side (SAS) triangle congruence postulate, we can see that triangles ABC and BCD are congruent because they share a side, angle, and side.
Finally, using the Side-Side-Side (SSS) triangle congruence postulate, we can conclude that triangles ACD and BDA are congruent because they have all three sides congruent.
Since corresponding parts of congruent triangles are congruent, we can conclude that AC is congruent to BD.
The probable question may be:
Given: ABCD is rectangle
Prove : AC is congruent to BD.
1. Definition of a rectangle
2. Reflexive property
3. Side-Angle-Side triangle congruence postulate
4. Side-Side-Side triangle congruence postulate
5. Corresponding parts of congruent triangles are congruent