Please check my answers
With two parallel lines cut by a transversal, the number of pairs of alternate interior angles is equal to the number of pairs of corresponding angles. (1 point)
Always
Sometimes
Never
*I think the answer is sometimes
Opposite angles in a quadrilateral are congruent. (1 point)
Always
Sometimes
Never
*I think the answer is never
Quadrilaterals have four pairs of opposite sides. (1 point)
Always
Sometimes
Never
*I believe the answer is never, I think they got 2
Convex quadrilaterals have two diagonals. (1 point)
Always
Sometimes
Never
*I believe the answer is always
To check your answers, let's go through each question one by one and explain how to determine the correct answer:
1. With two parallel lines cut by a transversal, the number of pairs of alternate interior angles is equal to the number of pairs of corresponding angles.
To determine the answer, you need to understand the properties of parallel lines and transversals. When two parallel lines are intersected by a third line (transversal), alternate interior angles are formed on opposite sides of the transversal and on the interior of the parallel lines. Corresponding angles are formed on the same side of the transversal but on different parallel lines.
Since the angles are formed in pairs, if the number of alternate interior angles is equal to the number of corresponding angles, then the answer is "Sometimes". This is because it depends on the specific arrangement and angles formed by the parallel lines and transversal. Therefore, your answer of "Sometimes" is correct.
2. Opposite angles in a quadrilateral are congruent.
To determine the answer, you need to understand the properties of quadrilaterals. Opposite angles are formed when two lines intersect, creating four angles in a quadrilateral. If opposite angles are congruent, it means that they have the same measure or size.
However, this statement is not always true for all quadrilaterals. There are quadrilaterals, such as kites or irregular quadrilaterals, where opposite angles may not be congruent. Therefore, the correct answer is "Sometimes". Your answer of "Never" is incorrect.
3. Quadrilaterals have four pairs of opposite sides.
To determine the answer, you need to understand the definition of a quadrilateral. A quadrilateral is a polygon with four sides. Opposite sides are those that do not share a vertex (corner) but are on the same straight line.
Since a quadrilateral has four sides, it means there are four pairs of opposite sides. Therefore, the answer is "Always". Your answer of "Never" is incorrect.
4. Convex quadrilaterals have two diagonals.
To determine the answer, you need to understand the properties of convex quadrilaterals. A convex quadrilateral is a quadrilateral where all interior angles are less than 180 degrees and all sides lie within the shape.
A diagonal is a line segment connecting two non-adjacent vertices of a polygon. In a convex quadrilateral, we can draw two diagonals connecting opposite vertices, dividing the shape into four triangles.
Therefore, the answer is "Always" since convex quadrilaterals always have two diagonals. Your answer of "Always" is correct.
Overall, you got two out of four answers correct.