Gr 10 Math Ch 6: Proofs and Conjectures

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Which property is used to demonstrate that triangles CDZ and ABX are congruent?

Side-Angle-Side (SAS)

Side-Side-Side (SSS)

Angle-Side-Angle (ASA)

Angle-Angle-Side (AAS) (correct)

What can be concluded about angles Mˆ2 and Oˆ2 in parallelogram MNOP?

Mˆ2 is greater than Oˆ2

Mˆ2 is less than Oˆ2

Mˆ2 and Oˆ2 are supplementary

Mˆ2 and Oˆ2 are equal (correct)

Which similarity criterion is used to prove that triangles XAM and ZCO are congruent?

Angle-Angle (AA)

Side-Side-Angle (SSA)

Angle-Angle-Side (AAS) (correct)

Angle-Side-Angle (ASA)

In proving that MNOP is a parallelogram, what conclusion is drawn from the equal angles Nˆ2 and Pˆ2?

Both pairs of opposite angles are equal. Signup and view all the answers

Which segments are shown to be equal in the proof of congruence between triangles CDZ and ABX?

DC and AB Signup and view all the answers

What geometric figure is MNOP established to be based on the conclusions drawn from the angle and side relationships?

Parallelogram Signup and view all the answers

What congruence criterion is used to establish that triangles CDZ and ABX are congruent?

AAS (Angle-Angle-Side) Signup and view all the answers

Which property allows the conclusion that Mˆ2 equals Oˆ2?

Vertical angles Signup and view all the answers

What is the first step in proving that triangles ADW and CBY are congruent?

Demonstrate that angle A and angle C are equal Signup and view all the answers

What conclusion can be drawn from the congruence of triangles XAM and ZCO?

Mˆ1 and Oˆ1 are equal Signup and view all the answers

Which property directly leads to MNOP being classified as a parallelogram?

Both pairs of opposite angles are equal Signup and view all the answers

What is demonstrated when it is shown that Nˆ2 equals Pˆ2?

Both pairs of opposite angles are equal Signup and view all the answers

Which statement is correct regarding the angle relationships in parallelogram ABCD and its bisectors?

Angle A and angle C are congruent due to parallel sides. Signup and view all the answers

In proving triangles XAM and ZCO are congruent, which reasoning is primarily used?

Angle-angle-side (AAS). Signup and view all the answers

What is the outcome when angle relationships in quadrilateral MNOP are compared?

Both pairs of opposite angles are equal, confirming it as a parallelogram. Signup and view all the answers

What geometric property is specifically utilized to conclude that triangles CDZ and ABX are congruent?

Angle-angle-side (AAS) postulate. Signup and view all the answers

What is necessary to show in order to prove that quadrilateral MNOP is a parallelogram?

Both pairs of opposite angles are equal. Signup and view all the answers

Which reasoning strategy is fundamental in proving angle Mˆ2 equals angle Oˆ2?

They are classified as vertical opposite angles. Signup and view all the answers