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Geometry – Chapter 8 Test Review Standards/Goals:

C.1.f.: I can prove that two right triangles are congruent by applying the LA, LL, HL, and HA congruence statements.

o I can prove right triangles are similar to one another. o I can solve problems dealing with right triangles that are congruent to one another.

D.2.d.: I can solve problems involving the relationships formed when the altitude to the hypotenuse of a right triangle is drawn.

G.SRT.4./ D.2.e.: I can apply the Pythagorean theorem and its converse to triangles to solve mathematical and real-world problems.

D.2.f.: I can identify and use Pythagorean triples in right triangles to find lengths of the unknown side.

E.1.g.: I can determine the geometric mean between two numbers and use it to solve problems.

H.1.a.: I can apply the properties of a 45-45-90 degree and 30-60-90 degree triangle to determine lengths of sides of triangles.

G.SRT.8: I can use properties of right triangles to solve problems, including ones that involve real-life applications.

G.SRT.6.: I can name the sides of a right triangle as they relate to one of the acute angles. o I can compare ratios for similar right triangles and understand the connection

between the ratio and the acute angle leading to trigonometric ratios. Algebra Standards:

G.1.b.: I can simplify radicals that have various indices.

G.1.f.: I can evaluate expressions and solve equations containing ‘nth’ roots or rational exponents.

IMPORTANT VOCABULARY

Radical Expression

Radical Radicand Perfect squares

Pythagorean Theorem

Converse of Pythagorean Theorem

Pythagorean Triple

Right triangles

Hypotenuse Geometric mean

Similarity statements

Altitude 30-60-90 degree triangles

45-45-90 degree triangles

LL HL HA LA

#1. Find a geometric mean between 7 and 9. #2. Do 19, 15, and 13, form a Pythagorean Triple? Why or why not? Explain.

Classify each triangle with the given side lengths as ACUTE, RIGHT, or OBTUSE.

#3. 3, 8, 10 #4. 12, 15, 19 #5. √ , √ , √

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What additional information do you need to prove that the following triangles are congruent by the given theorems? #6. HA #7. HL

Determine if the following pairs of triangles are congruent. If yes, state the reason from the following (LL, HA, HL, LA) #8. #9.

#10. #11.

#12. #13.

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#14. Complete the similarity statement for the following triangle:

∆RUS ∽ ∆SUT ∽ ∆_________ #15. In the figure shown above, what segment of the hypotenuse is adjacent to ̅̅ ̅̅ ? ________ #16. MULTIPLE CHOICE QUESTION: Determine which type of triangle’s sides can be found using the Pythagorean Theorem.

a. Acute Δ b. Scalene Δ c. Right Δ d. Obtuse ∆

Use the diagram to complete each statement:

#17.

#18.

#19.

#20.

#21. The playing surface of a football field is 300 ft long and 160 ft wide. If a player runs from one corner of the field to the opposite corner, how many feet does he run?

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Find the missing parts in the figures below: #22. #23.

#24. #25.

#26. If a leg = √ , find the hypotenuse. #27.

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#28. #29. Given: BD ⊥ AC; CD ⊥ AE; CD = 9; AD = 13

Algebra Review

#30. Simplify: √ √ #31. Simplify: √

#32. Simplify:

√ #33. Solve: √ = 9

#34. Solve: √ = √ #35. Simplify: √

#36. Solve: √ √ #37. Find the domain of: ( ) √

#38. Find the domain of: ( )

√ #39. For f(x) in #8, find f(27).

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#40. Suppose that TU = 3 RT and TS = 160. Find RT & TU.

#41. Imagine the Cartesian coordinate plane below represents a map. Each block represents 1 square mile. Imagine a person starts at point (-8, -7) and travels due north to point (-8, -2). Then, they travel due east to point (-3, -2). Next, they travel due north to (-3, 9). Finally, they travel due east to (10, 9). The person then returns to the starting point, taking the closest possible direct route. To the nearest MILE, how far has this person traveled? Use the graph below to assist you.

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