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
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