Quadrilaterals and Proofs Flashcard

Front

What is always true for a parallelogram?

Back

Opposite sides are congruent and parallel

Answer explanation

In a parallelogram, opposite sides are always congruent and parallel, which is a defining property. The other options do not hold true for all parallelograms.

Front

Back

Answer explanation

To find the slope (m) between points (x1, y1) and (x2, y2), use the formula m = (y2 - y1) / (x2 - x1). Here, m = (11 - 3) / (6 - 2) = 8 / 4 = 2. Thus, the slope is 2.

Front

Back

Answer explanation

To find the length of segment AB, use the distance formula: \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\). Here, \(A(1,2)\) and \(B(4,6)\) give \(d = \sqrt{(4-1)^2 + (6-2)^2} = \sqrt{9 + 16} = \sqrt{25} = 5\). Thus, the length is 5.

Front

Which statement is true about the diagonals of a rectangle?

Back

They are always congruent

Answer explanation

In a rectangle, the diagonals are always congruent, meaning they are of equal length. This is a defining property of rectangles, distinguishing them from other quadrilaterals.

Front

Which construction tool is essential for constructing a perpendicular bisector?

Back

Compass

Answer explanation

A compass is essential for constructing a perpendicular bisector as it allows you to draw arcs from both endpoints of a line segment, helping to find the midpoint and create the bisector accurately.

Front

Definition of a midpoint?

Back

The point that divides a segment into two congruent segments

Answer explanation

The correct definition of a midpoint is the point that divides a segment into two congruent segments, meaning both parts are equal in length. The other options do not accurately describe a midpoint.

Front

Back

Answer explanation

Since A, B, and C are collinear with B between A and C, we can find AC by adding AB and BC. Thus, AC = AB + BC = 7 + 5 = 12. Therefore, the correct answer is 12.

Front

Which theorem states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent?

Back

ASA

Answer explanation

The ASA (Angle-Side-Angle) theorem states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

Front

What is always true about vertical angles?

Back

They are congruent

Answer explanation

Vertical angles are formed by the intersection of two lines and are always congruent, meaning they have equal measures. Therefore, the correct choice is that they are congruent.

Front

Back

Answer explanation

To find the midpoint, use the formula: M = ((x1 + x2)/2, (y1 + y2)/2). For points (2, 5) and (8, 9), M = ((2 + 8)/2, (5 + 9)/2) = (5, 7). Thus, the midpoint is (5, 7).