University:
Missouri State University
Course:
MTH 460 | College Geometry
Academic year:

2021
Views:

468

Pages:

4
Author:

rehinhea0c

Geometry/Trigonometry II Name 5.2 Ways to Prove That Quadrilaterals are Parallelograms Review Definition of a parallelogram A quadrilateral with 2 pair of parallel sides is called a parallelogram. If AB//CD 40 11 BC, ther ABCD IS p-gram. Theorem 5-4 If both pair of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. opp. Sicles make a p-gram. T Proof Given: overline TS cong overline QR overline TQ equiv overline SR Prove: Quad QRST is a parallelogram Statement 1. TS cong Q*R_{i} TQSR 2 overline TR cong overline TR 3. Delta*QT R cong\ Delta SRT 4. angle QTR cong\ < TRS angle QRT equiv underline < RTS 5. TS|| QR and TQSR 6. Quad QRST is a parallelogram S H Q R 555 Reason 1. Given 2. Reflexive 3. SSS 4. CPCTC 5. Congruent, Alt. Int. Angles form Parallel Lines 6. Def.of a parallelogram Theorem 5-5 If one pair of sides of a quadrilateral are both congruent and parallel, then the quadrilateral is a parallelogram. SAS Theorem 5-6 If both pair of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. Theorem 5-7 If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. X *If X is the miept of both dragonals... Five Ways to Prove that a Quadrilateral is a Parallelogram ◆1. Show that both pair of opposite sides are parallel. 2. Show that both pair of opposite sides are congruent. 3. Show that one pair of opposite sides are both congruent and parallel. 4. Show that both pair of opposite angles are congruent. 5. Show that the diagonals bisect each other. You can find this list on pg 172 Examples: Complete the following with sometimes, always, or never: 1. The diagonals of a quadrilateral sometimes bisect each other. 2. If the measures of two angles of a quadrilateral are equal, then the quadrilateral is sometimes a parallelogram. If one pair of opposite sides of a quadrilateral is congruent and parallel, then the quadrilateral is always a parallelogram. 4. If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is always a parallelogram. 5. To prove a quadrilateral is a parallelogram, it is never opposite sides is parallel enough to show that one pair of 6. Determine if the information given will give you a parallelogram. If it does, name the parallelogram and state a reason why it is a parallelogram. If there is not enough information write none. G H 1. overline GH equiv overline KJ ; overline GK equiv overline HJ GHJK, b/c opp. sides are congruent 2. LKD:LIKJ LIJK, b/c of the def. of p-gram 3. M is the midpoint of overline GJ and overline HK GHJK, b/c diag's bisect each other K 4. angle KGl equiv angle GIH ; GHKJ none L I M J 5. LGTH; overline LG equiv overline IH GHIL, b/c one pair of sides is parallel and congruent