Question

use the given information to answer each question. explain your reasoning.
sample problem
tommy drew a quadrilateral. he used a protractor to measure all four angles of the quadrilateral.
how many pairs of angles must be congruent for the quadrilateral to be a parallelogram?
opposite angles are congruent in a parallelogram, so both pairs of opposite angles must be congruent.

simon connected a square and two congruent right triangles together to form an isosceles trapezoid.
draw a diagram to represent the isosceles trapezoid.
use the drawing tool to draw the diagram.
scribble

Explanation:

For the first question (Tommy's quadrilateral):

Step1: Recall parallelogram angle property

A parallelogram has opposite angles congruent. A quadrilateral has 4 angles, so there are 2 pairs of opposite angles.

Step2: Apply the property

Since in a parallelogram, opposite angles are congruent, we need 2 pairs of congruent opposite angles.

1. Draw a square. Let's say the square has vertices \( A, B, C, D \) in order.
2. Draw two congruent right triangles. Let the square have side length \( s \). The right triangles should have one leg equal to \( s \) (to attach to the square) and the other leg of some length \( l \).
3. Attach one right triangle to one side of the square (e.g., side \( AB \)) and the other congruent right triangle to the opposite side (e.g., side \( CD \)) such that the non - square sides of the triangles are parallel. The resulting figure will have a pair of parallel sides (the top and bottom sides formed by the square's top side and the hypotenuses of the triangles, or vice versa) and the non - parallel sides (the legs of the triangles and the other two sides) will be equal in length, forming an isosceles trapezoid.

(If a visual diagram was to be drawn, using the drawing tool, we would:

• First draw a square.
• Then draw two right triangles with the same leg length as the square's side and attach them to two opposite sides of the square, aligning them so that the figure has a trapezoidal shape with the two non - square sides being equal in length.)

Answer:

2 pairs

For the second question (Simon's isosceles trapezoid diagram):

(Note: Since it's a drawing request, here's a description of how to draw it)