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
I think there are twice as many pairs of corresponding angles as interior because exterior also correspond.
Yes of it is a parallelogram (including a rectangle). No is sides are all different lengths or for example a trapezoid.
Right
right
Draw two parallel lines cut by a transversal. Label all angles.
Identify the following on your diagrams
interior angles
exterior angles
alternate interior angles
alternate exterior angles
corresponding angles
To check your answers, let's review the properties of angles and sides in parallel lines and quadrilaterals.
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.
The correct answer is sometimes. To find the answer, we need to understand that when two parallel lines are cut by a transversal, alternate interior angles are formed. These angles are located on opposite sides of the transversal and between the two parallel lines. Corresponding angles are also formed on the same side of the transversal but outside the two parallel lines. In some cases, alternate interior angles and corresponding angles can be equal, such as when the parallel lines are perpendicular. However, in other cases, they may not be equal.
2. Opposite angles in a quadrilateral are congruent.
The correct answer is sometimes. Opposite angles in a quadrilateral are congruent when the quadrilateral is a parallelogram. In other quadrilaterals, such as a trapezoid or a kite, opposite angles may not be congruent.
3. Quadrilaterals have four pairs of opposite sides.
The correct answer is sometimes. Quadrilaterals can have four pairs of opposite sides when they are parallelograms. However, in other types of quadrilaterals, such as trapezoids or kites, only two pairs of opposite sides exist.
4. Convex quadrilaterals have two diagonals.
The correct answer is always. A convex quadrilateral is a quadrilateral with no interior angles greater than 180 degrees. For any convex quadrilateral, there are always two diagonals, which are the line segments connecting nonadjacent vertices.
Based on the explanations above, here are the corrections:
1. Sometimes (correct)
2. Sometimes (correct)
3. Sometimes (incorrect - they have two pairs of opposite sides)
4. Always (correct)
Please make the necessary changes to your answers.