ABCD is a parallegram.if AB =2AD and p CD middle point then descraibe m<ABP=90degree
To describe the measure of ∠ABP as 90 degrees, we can use the properties of a parallelogram and its diagonals.
In a parallelogram, opposite sides are equal in length and opposite angles are congruent.
Given that AB = 2AD, we can conclude that AB is twice the length of AD.
Since P is the midpoint of CD, we can also infer that CP = PD.
Now, let's consider the diagonal AC. Since AC bisects the parallelogram, it divides it into two congruent triangles, namely ΔABP and ΔADP.
Because AB is twice the length of AD, and CP is equal to PD, we can conclude that ΔABP is similar to ΔADP. (Side-Angle-Side Similarity Criterion)
As the triangles ΔABP and ΔADP are similar, we can conclude that the corresponding angles are equal. Therefore, ∠ABP is congruent to ∠ADP.
Since the opposite angles ∠ADP and ∠ADQ in a parallelogram are congruent, we have ∠ADP = ∠ADQ.
Considering that ∠ADQ is a right angle (90 degrees), we can conclude that ∠ADP is also 90 degrees.
Since ∠ABP is congruent to ∠ADP, we can state that ∠ABP is also 90 degrees.
In summary, the measure of ∠ABP is 90 degrees.