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Game season just finished. Four of the most 

competitive schools competed for the 

ultimate challenge: the Olympic Games. 

Various sports were included, such as; 

soccer,swimming, bike riding, tennis, and 

track. Although it is over, and the winner was 

given their price, the consecutive, Mr. 

Ramirez, whom is in charge of the Olympic 

Games, needs for the team of Dumm & 

Dummer to analyze the games, 

geometrically.. Mr. Ramirez gave the team 

Dumm & Dummer a clip board filled with the  

parts that will be analyzed.

Sections that are to be 

analyzed:

I. Probability & 

Statistics

II. Transformations

III. Angle Pair Relations

IV. Congruent Triangles

V. Similar Triangles & 

Trigonometry

VI. Polygons

VII. 3D Geometry

VIII. Circles

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To begin, the team Dumm & Dummer 

must find out several probabilities 

based off of the winning teams. 

From: Mr. Ramirez

To: Dumm & Dummer

 The following questions are to be answered, with 

an explanation. Due Friday.

1)What is the probability that Garey won Gold?

The Probability that Garey won is 17/61 = 

.28%

2) What is the probability that Ganesha won a 

medal?

The probability that Ganesha won a medal is 

40/161= .27%

3)What is the probability that Pomona won Gold & 

Bronze?

The probability that Pomona won Gold & 

Bronze is 28/106= .26% 

4) What is the probability that Diamond won 

silver? 

The probability that Diamond won Silver is 

0.16= 16%

JOSE, Juan, Ashley and Kaylah are competing 

for the 100 meter dash. The girls normally   end 

up up in second third. The boys end up in first 

or second, if we took out the boys from the 

race what would the probability that the girls 

won the race.

The Garey boys have a better average of winning 1st 

place than the girls in the 100 meter dash. What would 

the average be if the boys were taken out of the race?

P(GA.w1)11/20= 55%

P(B.w1)8/10=80%

P(G.w1)3/10=30%

If the boys were taken out, that means that the girls             

would have a 30% chance of winning first place. The       

boys have a better chance of winning first because                                         

they have an 80% chance if winning.                                                                                                                                                                                                                                  

Transformations! Dumm & Dummer must now figure out the 

steps that could have been taken for those who lost in the 

game of tennis. Did they reflect it wrong? Translate it?

Ariana, a Viking, was competing 

against a Pomona Devil. She 

missed the opposition's court, 

which effected her score. 

Ariana wonders where the ball 

would have landed if she 

would've hit it at a different 

angle.

(-2,-3) (-5,-3)

(-5,-6) (-2,-6)

Switch the signs of 

both number, 

however, leave their 

order the same.

(2,3) (5,3)

(5,6) (2,6)

(-2,-2) (-8,-2) (-2,-8) (-

8,-8)

In order to reflect the 

ball over the y axis, we 

simply flip the image. 

(2,-2) (-8,-2) (-2,-8) (-

8,-8)

(-2,-2) (-6,-2) (-2,-6) (-

6,-6)

In order to translate the 

ball, we simply move +5 

in the x-direction, and -

3 in the y- direction. 

(3,-5) (7,-5) (3,-9) (7,-

9)

Dumm & Dummer just 

finished their second 

quest, but that isn't the 

end. Now, they are 

being asked to figure 

out the angle pair 

relations of parallel/ 

perpendicular lines. 

Fabian, whom is in charge of the roads near the olympic 

stadium is worried. He needs to find the corresponding 

angles to these roads. There are new stores that will be built 

in the these new angles. He calls Dumm & Dummer in hope 

that they can help. 

Fortunately, they can and are on their way.

Dumm & Dummer explain that corresponding angles are angles 

that lie on two parallel lines that are cut off by a transversal. 

Although they are cut off, corresponding angles are still in 

the same position. 

a=e, b=f

Fabian is also concerned about finding the 

alternate Interior Angles to these roads. Dumm & 

Dummer explain how Alternate interior Angles are 

angles that lie on different parallel lines and on 

opposite sides of transversal 

c=f, d=e

Alternate Exterior Angles are angles that 

are congruent. They are two angles on 

opposite sides of a transversal, which lies 

on different parallel lines.

a=h, b=g

Lastly, Dumm and Dummer explain what 

Consecutive Interior Angles are to Fabian. 

These angles are supplementary. They are 

defined as two interior angles lying on the 

same side of the transversal cutting

 c=e, d=f 

Erick, a black panther, 

was devastated about 

his lose against Garey. 

He wants to figure out 

what the distance 

between him & his 

opponent was. Mr. 

Ramirez told the team 

Dumm & Dummer to 

figure out the answer 

to Erick's concern. 

They came up with the 

Distance Formula. 

To find the distance of two points, we 

must use the formula:

You simply then plug in the numbers, 

then solve.

Mr. Ramirez wonders how far the light of this stadium 

light can reach. He calls Dumm & Dummer and they 

come up with the Pythagorean Theorem. 

 They came up with the formula: 

Because the unknown side is the longest, also known as 

the hypotenuse, we plug it into c, and the other two 

numbers can go into a & b. You then solve and your 

answer comes out to be: 

138.924 = 139 ft. 

Mr. Rodriguez and his team have begun cleaning up and putting away everything. 

There's much to clean up, but he's particularly stuck on the cones. He needs to put 

all of them into isles, all the same size. He needs to figure out what cones are 

congruent to each other, and so he calls Dumm & Dummer, hoping they can figure 

out a way to solve the problem. They come up with the ASA, SSS & SAS 

Theorem's. 

The ASA Theorem states that if two angles and 

the included side of one triangle are equal to the 

other triangle, then both are congruent. 

CAB=ZXY (angle)

AB=XY (side)

ACB=XZY (angle)

The SAS Theorem (another way to see whether if two 

figures are congruent), states that if two sides are 

congruent to the other triangle, then both are congruent 

to one another.

AB=MO

BC=ON

The SSS Theorem is another way to see if 2   triangles are 

congruent to each other. 

In this case, AC is equal to EF, DE is equal to AB, & DF is equal 

to BC. Are these triangles equal though? 

Knowing this information, we can now pair up both 

triangles.

BC=28         7

DF= 20        5

DE=21         7

BA=15         5

EF=14         7

AC=10         5

As seen, all sides 

equal to each other, 

therefore we can 

say both triangles 

ARE similar to one 

another.

Polygons! Because many equipment is used during the 

Olympics are polygons, Mr. Ramirez wonder.., what are some 

characteristics these polygons have?

When two triangles have corresponding angles 

that are congruent, the triangles are similar.

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