Post on 18-Jan-2016
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
slide
Flip
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
Is this a flip a slide or a turn? ____________What corresponds to angle C? __________What corresponds to angle B? __________AX corresponds to __________________
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Naming Congruent Parts
Triangle TJD is congruent to Triangle RCF.List the congruent corresponding parts.Sides: ___________ ____________ __________Angles: _________ __________ __________
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j
d
r
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f
Naming Congruent Parts
Triangle WYS is congruent to triangle MKV. List the congruent corresponding parts.Use three letters to name each angle.
drawingSides: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 Justify4
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a
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Finding Congruent Triangles
Decide whether the triangles are congruent. Justify your answer.
Congruent Justify
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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
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b c
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e f
Proving Triangles Congruent
Given PQ congruent PS, QR congruent SR, <Q congruent <S, <QPR congruent SPRProve Triangle PQR congruent PSR
Statement Reason
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Proving Triangles Congurent
Given: < A congruent <D, <E congruent <C, AE congruent DC, EB congruent CB, BA congruent BDProve: Triangle AEB congruent DCB
Statement Reasona
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