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IdentifyingSimilarParts

Foreachproblem,listallofthematchingangles(singleletters)andallofthematchingsides(doubleletters).Then,createthethreefractionsets.1.

Angles Sides SideFractions

2.

Angles Sides SideFractions

3.△PQR~△ 𝐽𝑀𝐾

Angles Sides SideFractions

4.△ABC~△HGF

Angles Sides SideFractions

5.

Angles Sides SideFractions

6.

Angles Sides SideFractions

7.△KLN~△EHG

Angles Sides SideFractions

8.△PAC~△MAN

Angles Sides SideFractions

A

B

CD

E FGH IJ

K LMP N

XYZL

MN

SolvingProportionsForeachproblem,determinethevalueofx(startbycross-multiplying).

9. 2𝑥=1421 10.

𝑥5=1230

11. 69=8𝑥 12.

630

=𝑥25

13. 2

𝑥 + 8=69 14.

14=𝑥 − 712

15. 56=

15𝑥 + 2

16. 𝑥 − 43

=71

17. 4

𝑥 + 5=

3𝑥 − 2

18. 𝑥 + 73

=106

19. 𝑥 − 48

=𝑥 + 19

20. 912

=1

𝑥 + 2

Foreachproblembelow,pickafractionequationtouse,thenpluginthegiveninformationandsolveforx.21.△ABC~△LMN𝑳𝑵 = 𝟐𝟏,𝑩𝑪 = 𝟐,𝑴𝑵 = 𝟏𝟒,𝑨𝑪 = 𝒙

𝐴𝐵𝐵𝐶

=𝐿𝑀𝑀𝑁

𝐵𝐶𝐴𝐶

=𝑀𝑁𝐿𝑁

𝐴𝐵𝐴𝐶

=𝐿𝑀𝐿𝑁

22.△DEF~△PRQ𝑫𝑬 = 𝒙,𝑫𝑭 = 𝟓,𝑷𝑹 = 𝟏𝟐,𝑷𝑸 = 𝟑𝟎

𝐷𝐸𝐸𝐹

=𝑃𝑅𝑅𝑄

𝐸𝐹𝐷𝐹

=𝑅𝑄𝑃𝑄

𝐷𝐸𝐷𝐹

=𝑃𝑅𝑃𝑄

23.△RST~△AMY𝑺𝑻 = 𝟗,𝑨𝑴 = 𝟖,𝑹𝑺 = 𝟔,𝑴𝒀 = 𝒙

𝑅𝑆𝑆𝑇

=𝐴𝑀𝑀𝑌

𝑆𝑇𝑅𝑇

=𝑀𝑌𝐴𝑌

𝑅𝑆𝑅𝑇

=𝐴𝑀𝐴𝑌