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Definitions Congruent? Argue This Solve Me

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Row 1, Col 1

a2 + b2 = c2

In a right triangle, the square of the length of the hypotenuse is equal to the sum

of the squares of the lengths of the legs.

What is the Pythagorean Theorem?

1,2

No - Angle-Side-Side does NOT prove congruence.

Are these two triangles congruent?

1,3

If it is not sunny outside, I will not go running.

Original Statement: If it is sunny outside, I will go running. Find the inverse.

1,4

30-60-90 triangle:AC / 30 = 4 / 60

AC = 2

Solve for AC

2,1

If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle,

then the two triangles are congruent.

What is the Side-Angle-Side (SAS) theorem?

2,2

Yes - Angle-Angle-SideCongruence


2,3

The inverse of the statement will also be true.

If the converse of an original statement is TRUE, what else will also be true?

2,4

Sin(x) = 2.5 / 5Sin-1(2.5/5) = 30º

Solve for x

3,1

If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse

and a leg of a second right triangle, then the two triangles are congruent.

What is the Hypotenuse-Leg Theorem?

3,2

Yes - Side-Angle-Side congruence, or Angle-Angle-Side

congruence.


3,3

If I do not get an A on the test,I did not study.

Original Statement: If I study, I will get an A on the test. Find the contrapositive.

3,4

Tan(50) = AC / 3cmAC = 3.58 cm

Solve for AC

4,1

If two angles and the included side of one triangle are congruent to two angles and the

included side of a second triangle, then the two triangles are congruent.

What is the Angle-Side-Angle theorem?

4,2

Yes - Side-Angle-Side congruence.


4,3

The original statement will also be true.

If the contrapositive of an original statement is true, what else will also be true?

4,4

a = 6, b = 7 a2 + b2 = c2

36 + 49 = 85 = c2

C = 9.22

Solve for x

5,1

If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent.

What is the Angle-Angle-Side Theorem?

5,2

Yes - Angle-Angle-Side congruence.


5,3

If I wake up at 7:00 AM, I willmake it to the bus stop on time.

Inverse: If I do not wake up at 7:00 AM, I will not make it to the bus stop on time. Find the original statement.

5,4

(60 - d) + (x + d) +60 = 18060 - d + x + d + 60 = 180

120 + x = 180x = 60

Solve for x

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