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:
Step-by-step explanation:
Given the rational expression: , to express this in simplified form, we would need to apply the concept of partial fraction.
Step 1: factorise the denominator
Thus, we now have:
Step 2: Apply the concept of Partial Fraction
Let,
=
Multiply both sides by (x - 1)(x - 4)
=
Step 3:
Substituting x = 4 in
Substituting x = 1 in
Step 4: Plug in the values of A and B into the original equation in step 2