In quadrilateral ABCD, diagonals AC and BD bisect one another: What statement is used to prove that quadrilateral ABCD is a para
llelogram?
- Angles ABC and BCD are congruent.
- Sides AB and BC are congruent.
- Triangles BPA and DPC are congruent.
- Triangles BCP and CDP are congruent.
- Angles ABC and BCD are congruent.
- Sides AB and BC are congruent.
- Triangles BPA and DPC are congruent.
- Triangles BCP and CDP are congruent.
1 answer:
Answer:
Option D.
Step-by-step explanation:
In the figure attached, Diagonals AC and BD are bisecting each other at a point P.
That means AP ≅ CP and DP ≅ BP
We have to prove : AB ≅ DC and AB ║ DC
Proof : In triangles BPA and CPD,
AP ≅ CP
DP ≅ BP
∠ APB ≅ ∠DPC [vertically opposite angles]
Therefore, by postulate SAS [Side-Angle-Side]
ΔBCP ≅ ΔCDP
Option D. will be the answer.
You might be interested in
Answer:
x = 15
Step-by-step explanation:
The easiest way to solve this is to realise that a triangle takes up half the area of a rectangle of the same width and height.
We are told that the width of the triangle is 10, and that the line of length 10 is perpendicular to the longest side of the triangle. Because of that we know that x can be multiplied by ten to get the area of the rectangle that is twice the area of the triangle.
We are also told that the triangle's area is 75 units. With all of that put together, we can say: