Geometryyy

Translations

100

Point A(3,−2)A(3, -2)A(3,−2) is translated 4 units right and 5 units up.

What are the new coordinates?

A′(7,3)A'(7,3)A′(7,3)

200

Point B(−6,4)B(-6, 4)B(−6,4) is translated 2 units left and 7 units down.

(−6−2, 4−7)=(−8,−3) B′(−8,−3)B'(-8,-3)B′(−8,−3)

300

Translate point C(5,−1)C(5,-1)C(5,−1) using:

(x,y)→(x−3, y+6)(x,y) 

(5−3, −1+6)=(2,5) C′(2,5)C'(2,5)C′(2,5)

400

Triangle ABCABCABC has vertices:

• A(1,2)A(1,2)A(1,2)
• B(4,2)B(4,2)B(4,2)
• C(2,5)C(2,5)C(2,5)

Translate the triangle using:

(x,y)→(x+2, y−4)(x,y) (x+2,\ y-4)(x,y)→(x+2, y−4)

A′(3,−2) B′(6,−2)B'(6,-2)B′(6,−2) C′(4,1)C'(4,1)C′(4,1)

500

A video game character starts at (8,1)(8,1)(8,1). The character moves 5 spaces left and 9 spaces up.

Where does the character end up?

(8−5, 1+9)=(3,10)

(3,10)(3,10)(3,10)

Transversals

100

Two parallel lines are cut by a transversal.

One angle measures 70∘70^\circ70∘.

What is the corresponding angle?

Corresponding angles are equal.

70 degrees

200

One alternate interior angle is 115∘115^\circ115∘.

What is the other alternate interior angle?

Alternate interior angles are equal

115∘

300

One same-side interior angle is 100∘100^\circ100∘.

Find the other angle.

Same-side interior angles add to 180∘180^\circ180

80∘

400

One angle is 45∘45^\circ45∘.

Find its vertical angle.

Vertical angles are equal.

45∘ 

500

One angle is 140∘140^\circ140∘.

Find the angle next to it.

Linear pairs add to 180∘180^\circ180∘.

180∘

Slope

100

Find the slope between:

(2,3)and(5,9)

Slope=2

200

Find the slope between:

(1,7)and(4,1)

Slope=-2

300

Find the slope between:

(−3,2)and(1,10)

Slope=2

400

Find the slope between:

(6,5)and(6,−2)

Slope= Undefined

500

Find the slope between:

(0,4)and(8,4)

Slope=0

Pythagorean Theorem

100

A right triangle has legs of 3 and 4.

Find the hypotenuse.

5

200

A right triangle has legs of 5 and 12.

Find the hypotenuse.

13

300

A right triangle has legs of 8 and 15

17

400

The hypotenuse is 10 and one leg is 6.

Find the missing side.

8

500

The hypotenuse is 13 and one leg is 5.

Find the missing side.

12

Triangle Congruency Theorems

100

Triangle ABC and triangle DEF have:

• AB=DE
• BC=EF
• AC=DF

Are the triangles congruent? Which theorem?

SSS

200

Triangle JKL and triangle MNO have:

• JK=MN
• ∠K=∠N
• KL=NO

Are the triangles congruent?

SAS

300

Triangles have:

• ∠A=∠D
• AB=DE
• ∠B=∠E

Which theorem proves congruence?

ASA

400

Triangles have:

• ∠X=∠P
• ∠Y=∠Q
• XZ=PR

Which theorem proves congruence?

AAS

500

Two right triangles have:

• congruent hypotenuses
• one pair of congruent legs

Are the triangles congruent?

HL