Properties of Quadrilaterals and Congruence

Tom, a 14-year-old student, participates in a quiz contest focused on the properties of quadrilaterals. He faces three questions in the first stage, each requiring him to prove geometric theorems. The first question involves proving that triangles formed by a diagonal in a parallelogram are congruent. The second question requires proving that opposite sides of a parallelogram are equal. The third question challenges Tom to prove that diagonals bisect each other. Tom successfully answers all questions, demonstrating his understanding of geometry and motivating him for the next stage.

What is the main focus of the quiz Tom is participating in?

• Properties of circles

• Properties of polygons

• Properties of quadrilaterals

• Properties of triangles

How many stages does Tom need to pass in the quiz?

• Four

• Three

• Two

• One

What geometric shape is Tom's room in the first question?

• Parallelogram

• Square

• Rectangle

• Trapezoid

Which criterion did Tom use to prove the triangles congruent in the first question?

• S-A-S

• A-S-A

• R-H-S

• S-S-S

What does Tom need to prove in the second question?

• Diagonals are equal

• All sides are equal

• Opposite sides are equal

• Angles are equal

What method does Tom use to prove the opposite sides are equal?

• Using congruent triangles

• Using perpendicular lines

• Using similar triangles

• Using parallel lines

What is the hint given for proving opposite angles are congruent?

• Use parallel lines

• Use congruent triangles

• Use perpendicular lines

• Use similar triangles

What is Tom required to prove in the third question?

• Diagonals are parallel

• Diagonals are perpendicular

• Diagonals bisect each other

• Diagonals are equal

Which triangles does Tom use to prove the diagonals bisect each other?

• Triangle ABD and Triangle CBD

• Triangle ACD and Triangle BDC

• Triangle ABC and Triangle ADC

• Triangle ABE and Triangle DCE

What realization does Tom have after completing the first stage?

• Math is his favorite subject

• He needs more practice

• Theorems are easy with tools

• Geometry is difficult