Write an indirect proof to show that opposite sides of a parallelogram are congruent

Therefore, because corresponding parts of congruent triangles are congruent or by definition of congruent triangles. Have you done this in your proof?

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What if you added the diagonal to the diagram? Using substitution, we can say thatso therefore, the opposite angles of a parallelogram are congruent.

Questions Eliciting Thinking What do you know about this figure? WXYZ is a parallelogram so and because opposite sides of a parallelogram are congruent. Instructional Implications Provide the student with the statements of a proof of this theorem and ask the student to supply the justifications.

How can you show the two triangles are congruent? Provide another statement to be proven and have the student compare strategies with another student and collaborate on completing the proof. Examples of Student Work at this Level The student: Then, can be constructed and is unique since through two distinct points passes a unique line.

How can you show that the other pair is also congruent? Instructional Implications Challenge the student to prove other statements about parallelograms, squares, rectangles, and rhombi. WXYZ is a parallelogram so by definition.

Got It The student provides complete and correct responses to all components of the task. Using a colored pencil or highlighter, encourage the student to mark the statements which support the congruence theorem chosen. Questions Eliciting Thinking What is your general strategy for this proof?

WXYZ is a parallelogram so by definition and. Then, because of the SSS congruence theorem. Okaloosa Is this Resource freely Available? The congruence of one pair of angles or sides necessary to use the congruence theorem cited.

Then have the student analyze and describe the overall strategy used in the proof. Emphasize that a theorem cannot be used as a justification in its own proof.

Lesson Opposite angles of a parallelogram

Did you think of a plan for your proof before you started? Examples of Student Work at this Level The student fails to establish: Examples of Student Work at this Level The student provides a complete proof with appropriate justification such as: Encourage the student to begin the proof process by developing an overall strategy.

Using the Angle Addition Postulate we can say that and that. Can you show me all of the steps needed to apply the theorem you used? The uniqueness of Questions Eliciting Thinking How did you know you could add the diagonal to your diagram?

Did you include all of them in your proof?This Lesson (Proof of Opposite sides of a parallelogram are equal) was created by by chillaks(0): View Source, Show About chillaks: am a freelancer In this lesson we will prove the basic property of a parallelogram that the opposite sides in a parallelogram are equal.

Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.

terms used w.r.t. to theorems lc ord math theorem,axiom proof study guide by reckdun includes questions covering vocabulary, terms and more. then the angles opposite those sides are congruent.

Lesson Proof of Opposite sides of a parallelogram are equal

an equilateral triangle is also equiangular. How to write an Indirect Proof. Math Vocabulary, Theorems,& Postulates. STUDY. PLAY. you list the steps of the proof in the left column & write the matching reason for each step in the right column.

Proving Parallelogram Angle Congruence

right angle congruence theorem. if one pair of consecutive sides of a parallelogram are congruent, then the parallelogram is.

Write an indirect proof to show that opposite sides of a parallelogram are congruent. Be sure to create and name the appropriate geometric figures/5(11).

Two of the parallelogram proof methods use a pair of congruent sides. To complete one of these methods, you need to show one of the following: That the other pair of opposite sides are congruent.

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Write an indirect proof to show that opposite sides of a parallelogram are congruent
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