1 / 10

Properties and Theorems of Parallelograms Explained

This text outlines essential properties and theorems related to parallelograms, a type of quadrilateral. Key points covered include the congruence of opposite sides and angles, the supplementary nature of consecutive angles, and the fact that diagonals bisect each other. Theorems 6.2 to 6.5 provide fundamental insights into the characteristics of parallelograms, including practical examples for finding angle measures and unknown lengths. This concise guide serves as a resource for learning and applying the properties of parallelograms in geometry.

onan
Télécharger la présentation

Properties and Theorems of Parallelograms Explained

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 6.2 Properties of Parallelograms

  2. Q R P S Q R P S Q R P S Q R P S Theorem 6.2 If a quadrilateral is a parallelogram, then its opposite sides are congruent. PQ = RS and SP = QR Theorem 6.3 If a quadrilateral is a parallelogram, then it opposite angles are congruent. <P = < R and < Q = < S Theorem 6.4 If a quadrilateral is a parallelogram, then its consecutive angles are supplementary. m<P + m<Q = 180o, m<Q + m<R = 180o m<R + m<S = 180o, m<S + m<P = 180o Theorem 6.5 If a quadrilateral is a parallelogram, then its diagonals bisect each other. QM = SM and PM = RM _ _ _ _ ~ ~ ~ ~ _ _ _ _ ~ ~ Properties of Parallelograms

  3. Theorems • 6.2 If a quadrilateral is a parallelogram, then its opposite sides are congruent. • 6.3 If a quadrilateral is a parallelogram, then its opposite angles are congruent. Q R S P

  4. Theorems • 6.4 If a quadrilateral is a parallelogram, then its consecutive angles are supplementary. m<P + m<Q = 180° m<Q + m<R = 180° m<R + m<S = 180° m<S + m<P = 180° Q R S P

  5. Using Properties of Parallelograms • PQRS is a parallelogram. Find the angle measure. • m< R • m< Q Q R 70 ° + m < Q = 180 ° m< Q = 110 ° 70° P S

  6. 3 3 Using Algebra with Parallelograms • PQRS is a parallelogram. Find the value of h. 3h + 120 = 1800 - 120 -120 3h = 60 P Q h = 20 3h 120° S R

  7. Theorems • 6.5 If a quadrilateral is a parallelogram, then its diagonals bisect each other. R Q M P S

  8. Using properties of parallelograms • FGHJ is a parallelogram. Find the unknown length. • JH • JK 5 3 5 F G 3 K J H

  9. Examples • Use the diagram of parallelogram JKLM. Complete the statement. LM K L NK <KJM N <LMJ NL MJ J M

  10. Find the measure in parallelogram LMNQ. • LM • LP • LQ • QP • m<LMN • m<NQL • m<MNQ • m<LMQ 18 8 L M 9 110° 10 10 70° 9 P 8 70 ° 32° Q N 110 ° 18 32 °

More Related