Gr 10 Math Ch 6: Proofs and Conjectures

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Questions and Answers

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?

<p>Both pairs of opposite angles are equal. (D)</p> Signup and view all the answers

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

<p>DC and AB (C)</p> 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?

<p>Parallelogram (A)</p> Signup and view all the answers

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

<p>AAS (Angle-Angle-Side) (A)</p> Signup and view all the answers

Which property allows the conclusion that Mˆ2 equals Oˆ2?

<p>Vertical angles (C)</p> Signup and view all the answers

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

<p>Demonstrate that angle A and angle C are equal (C)</p> Signup and view all the answers

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

<p>Mˆ1 and Oˆ1 are equal (C)</p> Signup and view all the answers

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

<p>Both pairs of opposite angles are equal (B)</p> Signup and view all the answers

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

<p>Both pairs of opposite angles are equal (A)</p> Signup and view all the answers

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

<p>Angle A and angle C are congruent due to parallel sides. (A), Angle B and angle D are congruent due to alternate interior angles. (D)</p> Signup and view all the answers

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

<p>Angle-angle-side (AAS). (D)</p> Signup and view all the answers

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

<p>Both pairs of opposite angles are equal, confirming it as a parallelogram. (A)</p> Signup and view all the answers

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

<p>Angle-angle-side (AAS) postulate. (D)</p> Signup and view all the answers

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

<p>Both pairs of opposite angles are equal. (A), Both pairs of opposite sides are equal. (D)</p> Signup and view all the answers

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

<p>They are classified as vertical opposite angles. (A)</p> Signup and view all the answers

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