Question

PLZ HELP ASAP Given- ABCD is a trapezoid Prove: triangle AED is approximately triangle CEB

Answer 1

Answer:

The missing are:

1. ABCD is a trapezoid

2. Opposite sides in a trapezoid

3. Alternate interior angles are congruent

4. ∠DAE ≅ ∠BCA

5. AA postulate of similarity

Step-by-step explanation:

Let us revise the cases of similarity

1. AAA similarity : two triangles are similar if all three angles in the first triangle equal the corresponding angle in the second triangle  

2. AA similarity : If two angles of one triangle are equal to the corresponding angles of the other triangle, then the two triangles are similar.  

3. SSS similarity : If the corresponding sides of the two triangles are proportional, then the two triangles are similar.  

4. SAS similarity : In two triangles, if two sets of corresponding sides are proportional and the included angles are equal then the two triangles are similar.

In a trapezoid there is a pair of opposite parallel sides (not equal to each other)  

∵ ABCD is a trapezoid ⇒ Given

- From the figure the parallel sides are AD and BC

∴ AD // BC ⇒ Opposite sides in a trapezoid

- From the parallelism, there are alternate interior angles

   equal in measures

∴ ∠ADE ≅ ∠ CBD ⇒ Alternate interior angles are congruent

∴ ∠DAE ≅ ∠BCA ⇒ Alternate interior angles are congruent

- By using the 2nd case of similarity above

∴ Δ AED similar to Δ CEB ⇒ AA postulate of similarity

The missing are:

1. ABCD is a trapezoid

2. Opposite sides in a trapezoid

3. Alternate interior angles are congruent

4. ∠DAE ≅ ∠BCA

5. AA postulate of similarity