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 __________________

p

y

q

ra

x

b

c

Naming Congruent Parts

Triangle TJD is congruent to Triangle RCF.List the congruent corresponding parts.Sides: ___________ ____________ __________Angles: _________ __________ __________

t

j

d

r

c

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

43

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 SPRProve Triangle PQR congruent PSR

Statement Reason

p

q

r

s

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

b

c

d

e