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Geometry Name:__~-,--",,,,,,,,,,,~,,I':....- _ Examples: 4.1 - 4.4 Date: a Period:

4.1 p

In the figure, -

PQ ~ PS,PR .1 QS. Complete the sentence.

1. PQ is the J?L~Q~\,\£)q- of the right triangle f',.PQR.

2. In f',.PQR, PQ is the side opposite angle _L_..!...~---30- _ 3. QS is the Bo. 1;)9 ~ of the isosceles triangle f',.PQS.

4. T~legs of f',.PRS are PR and Q:s . Q R s 5. QS is the hypotenuse of f',.PRS.

Classify the triangles by (a) its angles and (b) its sides. ~

6 7 8 'j\~ 9. 100 0

Match the triangle description with the most specific name. 1O. Side lengths: 2, 3, 4 ~ . Equilateral

'----"' 11. Side lengths: 3, 2, 3 ~ calene 12. Side lengths: 4,4,4 --a btuse 13. Angle measures: 60,60, 60 ~ Equiangular 14. Angle measures: 30,60,90 l= E. Isosceles 15. Angle measures: 20, 145, 15c F. Right

Complete the statement using always, sometimes or never. 16. An isosceles triangle is S an equilateral triangle. 17. An obtuse triangle is S an isosceles triangle. 18. An interior angle ofa triangle and one of its adjacent exterior angles are B supplementary. 19. The acute angles of a right triangle are ------&..-- complementary. 20. A triangle N has a right angle and an obtuse angle.

Find the measure of the numbered angles. Find the measure of the exterior angle shown. 21. 22. lOb

2x-8

x 31 95

. ,----. X+ 3l -:.~x -8 -x -x 8

. 40 V L_16~· . a) DJ::,.l A.!o b)---"""'!~~~!C,ooI\,~

4.2

/:,LlvfN ==/:,PQR. Find the following. --------..,--------0

b-----------'"'=---"o

8. List the 6 Q1. mLP= \ S~ corresponding

2. LM== t-Q N congruent partsL-L ~ ~p3. LR==~

4. mLN= 3D~

5.PQ~~1 6. LN=~ R

M7. QR== ff\"" L:Ngep;:

9) Name the four methods you have learned for proving triangles congruent. Only one of these is called a theorem. Why is it called a theorem? . SS~ SE\i$ ~~ crn~~ 'ba:.. QS'-~"-"'-'I:

~ - "­Is it possible tp prove that the triangles are congruent? If so, state the postulate or theorem you would. use? 10) /:,RST == /:,TQR /:,JKL == /:,NML 12) /:,DFE == /:,JGH N

:~~~\NJ GL-JH

Q

/:,ABC == /:,DEF using the irndicated

13) ASA Congruence Postulate 14) AAS Congruence Theorem F

c -

AAA.B D

LOGICAL REASONING: Is it possible to prove that the triangles are congruent? If so, state the postulate or theorem you would use. Also state the congruent triangles. 15) R 16) ~ 17) B

P . s

T

SPtS

x

State the third congruence that must be given to prove that .postuBate or theorem.

E

B F A @o<~----r--'i3

U T

s

J~M J.-J.-_--V N

20)18)

L

Q

N~ ~~\

z

y

w

I •

LOGICAL REASONING: Decide whether enough information is given to prove that the triangles are congruent. If there is enough illlformation~ teU which congmence postulate or theorem you would use. 21) .D.ABC, .D.DEC 22) .D.FGH, .D.JKH 23) .D.PQR, .D.SRQ

A B F P Q

M G SSS E' D K

sSf\S ~\

J R 24) .D.UVT, .D.WVT 25) .D.LMN, .D.TNM 26) .D.YZW, .D.YXltV

L zT

w

x Nw U M

Vv

N StTS 27) .D.ACB, .D.ECD 28) .D.RST, .D.WVU 29) .D.GJH, .D.HLK

T UA J G

S~ @----'-~--~.........-_0' W Ho--+--nn--+"--';::>e>K

R r\} ~ S"' ~ ,v DEVELOPING PROOF: State the third congruence that must be given to prove that .D.PQR 2!:..D.STU using the indicated postulate or theorem. (Hint: First sketch .D.PQR and .D.STU. Mark the triangles with

the given information.) , L h. ~ L-U n Ii-30) Given: LQ 2!:. LT , PQ 2!:. ST, Use the AAS Congruence Theorem. N S ~

- - ~p-;::..~ 31) Given: LR 2!:. LU , PR ~ SU. Use the ASA Congruence Postulate. .-or- u 32) Given: LR 2!:. L U , L P 2!:. LS. Use the ASA Congruence Postulate. ~ ~"0S J

33) Given: PR ~ SU, LR 2!:. LU. Use the SAS Congruence Postulate.

_ N --- .

b~ ~ --nJ , Use the diagram. Name the indua€d angle between each pair of sides given.

34) JK and KL ~ L35) LP and LK L~U' 36) KL and JL L:rL ~ 37) PK and LK LL~!V 38) JL and JK L:] 39) KP and PL L?

40) Use the same diagram to list the 6 corresponding congruent parts.

E

K f!ff'----<!1

0----~

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