The question says:
Two pairs of touching sides are the same length. The diagonals meet at right angles. Opposite sides are not parallel.
The diagonals bisect each other, but are different lengths. The diagonals do not meet at right angles. Angles are not right angles.
Please could someone explain this, as I don't understand.
The first one is a kite shape.
The second one is a parallelogram.
In both problems sketch them first as described in the given information and then look for congruent triangles.
Thank you for your help.
Let's break down the two statements you provided and explain each one separately:
Statement 1: "Two pairs of touching sides are the same length. The diagonals meet at right angles. Opposite sides are not parallel."
This statement describes a parallelogram. A parallelogram is a type of quadrilateral (four-sided polygon) where opposite sides are parallel. In this case, it is stated that the opposite sides are not parallel, which means it cannot be a parallelogram. However, the statement also mentions that two pairs of touching sides are the same length. This suggests that it is a special type of quadrilateral known as a rectangle. A rectangle has four right angles (90-degree angles) and opposite sides of equal length. So, we can conclude that the shape being described is a rectangle.
Statement 2: "The diagonals bisect each other but are different lengths. The diagonals do not meet at right angles. Angles are not right angles."
This statement describes a different type of quadrilateral. It states that the diagonals bisect each other, meaning that they divide each other into two equal parts. It also mentions that the diagonals are different lengths, so we can rule out a rhombus where the diagonals are always equal in length. Furthermore, it states that the diagonals do not meet at right angles, indicating that it cannot be a square or a rectangle. Finally, it mentions that the angles are not right angles, eliminating the possibility of a square or rectangle again. Based on these clues, the shape being described is a kite. A kite is a quadrilateral with two pairs of adjacent sides that are equal in length, and the diagonals bisect each other but do not meet at right angles.
In summary, the first statement describes a rectangle, while the second statement describes a kite. Each statement provides specific characteristics and properties of the shape being described, allowing us to identify the shape accurately.