GeometryChapter4TestReview Name 1. Writeinthevaluesofanymissingangles,thenclassifyeachtrianglebyitsanglesandsides.a. b. c.

2. Solveforthevalueofeachvariable.Writethemeasureofeachangleinthediagram.

a. b.

3. Solveforeachoftheindicatedvalues.𝑥 = 𝑚∠1 = 𝑚∠2 = 𝑚∠3 = 𝑚∠4 = 4. Solvefor𝑥thenfindthemeasureoftheexteriorangleshown.

𝑥 = ExteriorAngle=

5. LabelthediagramandmarkallcongruentcorrespondingpartsinthediagramattherighttoshowΔ𝐺𝐻𝐹 ≅ Δ𝐴𝐸𝐾andcompletethestatements.

𝐺𝐻 ≅ ∠𝐺 ≅ Δ𝐹𝐺𝐻 ≅

𝐺𝐹 ≅ ∠𝐻 ≅

𝐻𝐹 ≅ ∠𝐹 ≅ Whatisthereasonallofthesecongruencestatementsaretrue?

6. Solveforeachvariable.a. b.

c. d.

7. Determineifitispossibletoprovethetrianglescongruent.Ifso,statethecongruenttrianglesand

givethereasonwhytheyarecongruent.Ifitisnotpossible,explainwhy.a. b. c.

Possible: Yes No Possible: Yes No Possible: Yes No

ΔCongruence ΔCongruence ΔCongruence

Reason Reason Reason

d. e. f.

Possible: Yes No Possible: Yes No Possible: Yes No

ΔCongruence ΔCongruence ΔCongruence

Reason Reason Reason

116°x°D

E

F x°

y°112°

y°x°

8. Writeaproof.a. Given:Labeledinpicture b. Given:𝐴𝐶 ≅ 𝐷𝐹,𝐴𝐵 ≅ 𝐷𝐸 Prove:Δ𝐷𝐵𝑀 ≅ Δ𝐶𝐴𝑀 Prove:𝛥𝐴𝐵𝐶 ≅ 𝛥𝐷𝐸𝐹

c. Given:𝐵𝐶 ≅ 𝐸𝐶,∠𝐵 ≅ ∠𝐸 d. Given:𝑆𝑅bisects∠𝑇𝑆𝑄,∠𝑇 ≅ ∠𝑄 Prove:Δ𝐴𝐵𝐶 ≅ Δ𝐷𝐸𝐶 Prove:Δ𝑅𝑇𝑆 ≅ Δ𝑅𝑄𝑆

e. Given:Labeledinpicture f. Given:𝑆𝑅 ≅ 𝑇𝑉, 𝑆𝑇 ≅ 𝑅𝑉 Prove:𝐴𝐷 ≅ 𝐴𝐶 Prove:∠𝑆 ≅ ∠𝑉

A

B E

D

C F

A

B

C

E

D

Q

S

T

R