Answer:
True
Step-by-step explanation:
Let us consider a parallelogram ABCD in which AB=CD and AD=BC.
Now, from ΔABC and ΔBAD, we have
AD=BC (Opposite sides of parallelogram)
BD=AC (Given)
AB=BA (common)
Thus, by SSS rule of congruency,
ΔABC≅ΔBAD.
Now, by corresponding parts of congruent triangles, we have
∠ABC=∠BAD.
But, we know that ∠ABC and ∠BAD forms the corresponding angle pair, thus ∠ABC+∠BAD=180°
⇒2∠ABC=180
⇒∠ABC=90°
Since they are interior angles of parallel lines AC and BC on the same side of their common secant AB. They are therefore both right, and ABCD is a rectangle.
Hence, the statement If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle is true.
Answer:
E-F and E-D
C-B and C-D
Step-by-step explanation:
The circle and triangle are as shown. The options are:
By drawing radius lines from the center of the circle to the tangent points B, D, and F, we can divide the triangle into 3 kites. Therefore, only segments that are legs of the same kite are congruent. So the answer must be E-F and E-D, and C-B and C-D.
