JeopardyType of Triangle

Angles in a Triangle

Congruent Triangles?

Sides + Angles =

Congruent?Misc.

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Final Jeopardy

$100 Question from “Type of Triangle?”

Triangle ABC has the following angle measures:

m<A = 60 m<B = 60m<C = 60

What type of triangle is ABC?

$100 Answer from “Type of Triangle”

An equiangular triangle (bonus $100 if you said equiangular AND acute)

$200 Question from “Type of Triangle”

What type of triangle is pictured below. You must classify it both by its angles AND by its side

$200 Answer from “Type of Triangle”

Isosceles Obtuse Triangle.

$300 Question from “Type of Triangle”

What type of triangle is ABE? Classify it both according to ANGLES and according

to SIDES.

$300 Answer from “Type of Triangle”

Isosceles Right Triangle

$400 Question from “Type of Triangle”

$400 Answer from “Type of Triangle”

1. Isosceles Obtuse Triangle

2. 50 – 2x = 12x + 22 yields…. x = 2

$500 Question from “Type of Triangle”

Classify Triangle EDB according to its angles AND its sides.

$500 Answer from “Type of Triangle”

Scalene Right Triangle

$100 Question from“Angles in a Triangle ”

What is the measure of <1?

$100 Answer from“Angles in a Triangle”

m<1= 83.1 degrees

$200 Question from“Angles in a Triangle”

Find x, y, and z.

$200 Answer from“Angles in a Triangle”

x = 70

y = 110

z = 30

$300 Question from “Angles in a Triangle”

$300 Answer from “Angles in a Triangle”

x = 180 – 70 – 30 = 80 degrees by the triangle angle sum theorem.

y = 80 degrees because of x and y are vertical angles

$400 Question from “Angles in a Triangle”

In the picture below– determine which angles (1, 2, 3, etc….) are exterior angles.

Then, for each exterior angle, determine the remote interior angles for that specific exterior angle.

$400 Answer from“Angles in a Triangle”

Exterior angles: < 8, <6 and <5

Remote interior angles for <8 and <6: <1 and <2

Remote interior angles for <5: <1 and <3

$500 Question from“Angles in a Triangle”

Billy claims that m<8 = m<1 + m<2. Is he correct? Why or why not? **If you claim he is correct you must justify why using a theorem.

$500 Answer from“Angles in a Triangle”

He is correct because of the Exterior Angle Theorem. <8 is an exterior angle and so it’ll equal the sum of the two remote interior angles to it (i.e. <1 and <2)

$100 Question from “Congruent Triangles?”

Complete the congruence statement

$100 Answer from “Congruent Triangles?”

Triangle FCB

$200 Question from “Congruent Triangles?”

Determine x and y. Bonus $100 if you can classify the triangle on the

left by angles

$200 Answer from “Congruent Triangles?”

y= 40

x = 35

Acute Triangle

$300 Question from “Congruent Triangles?”

$300 Answer from “Congruent Triangles?”

$400 Question from “Congruent Triangles?”

$400 Answer from “Congruent Triangles?”

$500 Question from “Congruent Triangles?”

Find x and y.

$500 Answer from “Congruent Triangles?”

x = 13y = -1

$100 Question from “Sides + Angles = Congruent?”

Bobby claims that two triangles are congruent

because the angles of the two triangles are congruent. Is he correct? Why or why not?

$100 Answer from “Sides + Angles = Congruent?”

NO. He is incorrect because AAA isn’t a justification for congruent triangles.

$200 Question from “Sides + Angles = Congruent?”

Are the following Triangles congruent? Why or why not?

$200 Answer from “Sides + Angles = Congruent?”

Yes because of ASA and Vertical Angles Theorem.

$300 Question from “Sides + Angles = Congruent?”

Are triangles QPS and RPS congruent? Why or why not?

$300 Answer from “Sides + Angles = Congruent?”

No! A-S-S is not a justification for two triangles to be congruent!

$400 Question from“Sides + Angles = Congruent?”

If ZV and XU are congruent, are triangles ZWU and XWV congruent? Why or why

not?

$400 Answer from “Sides + Angles = Congruent?”

Yes! By ASA and the reflexive property

$500 Question from “Sides + Angles = Congruent?”

Is Triangle ABC congruent to Triangle DCB? Why or why not?

$500 Answer from “Sides + Angles = Congruent?”

They are congruent by AAS (or SAA)

$100 Question from “Misc.”Assume <1 is congruent to <2. To prove triangles ABC and CDA are congruent by SAS, what additional piece of information do we need?

$100 Answer from “Misc.”

CD is congruent to

CB

$200 Question from “Misc.”

Which pairs of Triangles are congruent? Justify your answers.

$200 Answer from “Misc.”

Pair One is congruent because of AASPair Two is congruent because of AASPair three is congruent because of AAS Pair Four is congruent because of ASA.

$300 Question from “Misc.”Assume <1 is congruent to <2. What other piece of information could be used to prove the triangles are congruent? Hint** There may be more than one***

$300 Answer from “Misc.”

AAS: <B is congruent to <DSAS: BC is congruent to DCASA: <BAC is congruent to <DAC

$400 Question from “Misc.”In the following picture, <M is congruent to

<H because of what theorem?

$400 Answer from “Misc.”

3rd Triangle Theorem.

$500 Question from “Misc.”

Triangle ABC and DEF have three congruent parts. Two sides and one angle. Problem is, we don’t know which angles

are congruent or which sides are congruent. Do we know for sure that the

triangles are congruent? Why or why not?

$500 Answer from “Misc.”

No--- the set up of the angles/sides could be such

that we get A-S-S. No good.

Final Jeopardy

Given: <Z is congruent to <C Line segment AK bisects <ZAC

Prove: Triangle ZAK is congruent to Triangle CAK

Final Jeopardy Answer

1. <Z is congruent to <C 1. Given AK bisects ZAC 2. <ZAK is congruent to <CAK 2. Definition of

angle bisector

3. AK is congruent to AK 3. Reflexive Property

4. Triangle ZAK is congruent to 4. AAS Triangle CAK