Congruent Figures Academic Geometry

Congruent Figures Congruent figures have the same size and shape. When two figures are congruent, you can move one so that it fits exactly on the other one.

Congruent Figures Three ways to make such a move – a slide, a flip, a turn Flip slide turn

Congruent Figures Congruent polygons have congruent corresponding parts – their matching sides and angles. Matching vertices are corresponding vertices. When you name congruent polygons, always list corresponding vertices in the same order.

Congruent Figures p y q r a x b c Is this a flip a slide or a turn? ____________ What corresponds to angle C? __________ What corresponds to angle B? __________ AX corresponds to __________________

Naming Congruent Parts j d r c f Triangle TJD is congruent to Triangle RCF. List the congruent corresponding parts. Sides: ___________ ____________ __________ Angles: _________ __________ __________

Naming Congruent Parts Triangle WYS is congruent to triangle MKV. List the congruent corresponding parts. Use three letters to name each angle. drawing Sides: Angles:

Finding Congruent Triangles Two triangles are congruent when they have three pairs of congruent corresponding sides and three pairs of congruent corresponding angles.

Finding Congruent Triangles Decide whether the triangles are congruent. Justify your answer. Congruent Justify 4 3 b a c d e

Finding Congruent Triangles Decide whether the triangles are congruent. Justify your answer. Congruent Justify j k l m n

Theorem 4-1 If two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent. Angle C is congruent to Angle F a b c d e f

Proving Triangles Congruent Given PQ congruent PS, QR congruent SR, <Q congruent <S, <QPR congruent SPR Prove Triangle PQR congruent PSR Statement Reason p s q r

Proving Triangles Congurent Given: < A congruent <D, <E congruent <C, AE congruent DC, EB congruent CB, BA congruent BD Prove: Triangle AEB congruent DCB Statement Reason c b a d e