4-6Congruence in Right Triangles

1 card

VocabularyRight Triangles

Leg

Leg

HypotenuseA

CB

Hypotenuse-Leg Theorem(HL)

If the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the triangles are congruent.

Then ABC DEF

If:

FE

D

CB

A

Ex 1:Which are congruent by HL?

3in3in

5in

5in

5in

3in

J

HG

FE

D

A

CB

Ex 1:Which are congruent by HL?

3in3in

5in

5in

5in

3in

J

HG

FE

D

A

CB

HFJ DEG

Ex 2: Prove the trianglesare congruent

R

QP

S

Ex 2: Prove the trianglesare congruent

R

QP

S Given

1. QPR and SRPare right, SP RQ

Ex 2: Prove the trianglesare congruent

R

QP

S Given

2. QPR SRP

1. QPR and SRPare right, SP RQ

Ex 2: Prove the trianglesare congruent

R

QP

S Given All Right angles

are congruent

2. QPR SRP

1. QPR and SRPare right, SP RQ

Ex 2: Prove the trianglesare congruent

R

QP

S Given All Right angles

are congruent3. PR PR

2. QPR SRP

1. QPR and SRPare right, SP RQ

Ex 2: Prove the trianglesare congruent

R

QP

S Given All Right angles

are congruent Reflexive

3. PR PR

2. QPR SRP

1. QPR and SRPare right, SP RQ

Ex 2: Prove the trianglesare congruent

R

QP

S Given All Right angles

are congruent Reflexive

4. SRP QPR

3. PR PR

2. QPR SRP

1. QPR and SRPare right, SP RQ

Ex 2: Prove the trianglesare congruent

R

QP

S Given All Right angles are

congruent Reflexive HL

4. SRP QPR

3. PR PR

2. QPR SRP

1. QPR and SRPare right, SP RQ

Ex 3: What else do you need to prove the triangles are congruent?

V T

R

X

Ex 3: What else do you need to prove the triangles are congruent?

V T

R

X

Is RT XT? orIs XV TV?

Ex 4: Prove the two triangles are congruent

T is the midpoint of RV

V

R

U

TS

Ex 4: Prove the two triangles are congruent

1. Given

T is the midpoint of RV

V

R

U

TS

1. T is the midpoint of RVS and U are right anglesRS TU

Ex 4: Prove the two triangles are congruent

1. Given

T is the midpoint of RV

V

R

U

TS

1. T is the midpoint of RVS and U are right anglesRS TU

2. RT TV

Ex 4: Prove the two triangles are congruent

1. Given

2. Definition of a midpoint

T is the midpoint of RV

V

R

U

TS

1. T is the midpoint of RVS and U are right anglesRS TU

2. RT TV

Ex 4: Prove the two triangles are congruent

1. Given

2. Definition of a midpoint

T is the midpoint of RV

V

R

U

TS

3. RST TUV

1. T is the midpoint of RVS and U are right anglesRS TU

2. RT TV

Ex 4: Prove the two triangles are congruent

1. Given

2. Definition of a midpoint

3. HL

T is the midpoint of RV

V

R

U

TS

3. RST TUV

1. T is the midpoint of RVS and U are right anglesRS TU

2. RT TV