Geo Topic 4 Review

Geo Topic 4 Review

Multiple Choice

If given the coordinates of a quadrilateral, using the distance formula to find the lengths of the diagonals will allow you to prove if it is a parallelogram.

• True, if they're congruent then it's a parallelogram

• True, if they're congruent then it's a rectangle

• False, you should find the opposite sides' slopes for it to be a parallelogram

• False, you should find the opposite sides' slopes for it to be a rhoombus

Multiple Choice

Which statement is sufficient to prove that quadrilateral ABCD is a parallelogram?

• One pair of sides is congruent

• One pair of sides is parallel

• The diagonals are perpendicular

• The diagonals bisect each other

Coordinate Proofs

• CHECK THE DIAGONALS!!!!

• If they're congruent--> rectangle

• If they're perpendicular--> rhombus (make sure to then check at least one pair of opposite sides are parallel so you know it's not a kite)

• If they're both--> square

Coordinate Proofs (cont.)

• Parallel slides have the SAME SLOPE

• Perpendicular slides have OPPOSITE RECIPROCAL SLOPES

•  $m=\frac{y_2-y_1}{x_2-x_1}$  

Multiple Choice

What's the most specific name for a quadrilateral with coordinates (-3,5), (3,7), (6,-2), (0,-4)

• Rectangle

• Square

• parallelogram

• kite

Fill in the Blanks

Multiple Select

ABCD has coordinates A(1,6) B(5,6), C(5,2). What has to be true about diagonal BD in order for this to be a square?

• BD should have a length of

  $4\sqrt{2}$

• BD should have a slope of -1

• BD should have a length of 4

• BD should have a slope of 1

Multiple Choice

Given coordinates A(0,0), B(3,4) and C(6,0), what must be true about triangle ABC?

• It is a right triangle with AB perp to BC

• It is a right triangle with AB perp to AC

• It is isosceles with AB congruent to BC

• It is isosceles with AB congruent to AC

Multiple Choice

Find the values of x and y

• x =4, y=12

• x=10, y=2

• x=4, y=9

• x=9, y=4

Fill in the Blanks

Multiple Choice

In quadrilateral ABCD, AB is parallel to CD. What else do you need to know to prove that ABCD is a parallelogram?

• The given information is sufficient

• The lengths of AB and CD are equal

• The slopes of BC and AD are equal

• The lengths of BC and AD are equal

Fill in the Blanks

Fill in the Blanks

Multiple Choice

In rectangle ABCD, BE= y + 4 and BD is 4y +2. Which of the following is true?

• CE = 7

• AC=7

• DE= 14

• AE=14

Multiple Choice

Write the equation of a line that is parallel to 8x - 3y = 24 and passes through the point (5, 8).

• 3y - 8x = -16

• 3y + 8x = -16

• 8x - 3y = 8

• 8x +3y = 5

Make sure you know...

• If a diagonal of a quadrilateral results in two CONGRUENT triangles, the ONLY thing you can say FOR SURE is that the figure is a parallelogram

• You don't know anything about the sides being perpendicular, congruent, etc.

Which triangles are congruent?