Plane Shapes Quiz

In a parallelogram, opposite angles are equal. This means that if we have two pairs of opposite angles, they will have the same measure. This property is a fundamental characteristic of parallelograms and can be proven using geometric theorems and properties. Therefore, the statement "The opposite angles in a parallelogram are equal" is true. The answer "true" and "t" both indicate the same correct response.

A quadrilateral is a polygon with four sides. The sum of all interior angles in any polygon is given by the formula (n-2) * 180 degrees, where n is the number of sides. In the case of a quadrilateral, n is 4, so the sum of its interior angles is (4-2) * 180 degrees = 2 * 180 degrees = 360 degrees.

A rectangle has two axes of symmetry. This means that it can be divided into two equal halves by two different lines. One axis of symmetry runs horizontally through the center of the rectangle, dividing it into two equal halves vertically. The other axis of symmetry runs vertically through the center of the rectangle, dividing it into two equal halves horizontally. Therefore, a rectangle has two axes of symmetry.

A triangle that has no sides the same length is called a scalene triangle. This means that all three sides of the triangle have different lengths. The term "scaleen" mentioned in the options is likely a misspelling or a variation of the correct term "scalene".

The correct answer is "trapezium". A trapezium is a quadrilateral with one pair of parallel sides. The other options, "trapeseum" and "trapizium", are misspellings of the word "trapezium".

A rectangle is a quadrilateral because it has four sides and four angles. A quadrilateral is a polygon with four sides, and a rectangle fits this definition. The opposite sides of a rectangle are parallel and equal in length, and all angles are right angles. Therefore, a rectangle can be classified as a quadrilateral.

This statement is true because all squares are rhombuses. A square is a special type of rhombus where all four sides are equal in length and all four angles are right angles. Therefore, every square can be classified as a rhombus, but not every rhombus can be classified as a square.

An equilateral triangle is a triangle in which all three sides are equal in length and all three angles are equal. Since the question asks for the size of angles in an equilateral triangle, the correct answer is 60 degrees.

A square is the only shape among the given options that has equal diagonals that bisect each other at right angles. In a square, all four sides are equal in length, and its diagonals are also equal. Moreover, the diagonals of a square intersect each other at a 90-degree angle, dividing the square into four congruent right triangles. Therefore, a square satisfies the given condition, making it the correct answer.

A kite has two pairs of parallel sides. One pair consists of the longer sides (the top and bottom edges), and the other pair consists of the shorter sides (the left and right edges). These parallel sides give the kite its distinct shape and symmetry.

A right-angled isosceles triangle is the best name for this triangle because it has one right angle and two equal sides. The term "right-angled" describes the presence of a right angle, while "isosceles" indicates that two sides of the triangle are equal in length. This name accurately describes the unique characteristics of this particular triangle.

The statement is false because the diagonals of a parallelogram are not always equal. While opposite sides of a parallelogram are equal in length, the diagonals can have different lengths. This can be observed by drawing different parallelograms and measuring their diagonals. Therefore, the correct answer is false.

The diagonals of a rhombus are not equal. A rhombus is a quadrilateral with all sides of equal length, but the diagonals are not necessarily equal. The diagonals of a rhombus bisect each other at right angles, but their lengths can be different.

A square is a type of quadrilateral, which means it has four sides. However, what distinguishes a square from other quadrilaterals is that all of its sides are equal in length. In addition to this, a square also has four right angles, meaning each angle measures 90 degrees. Therefore, the correct answer is "Is a quadrilateral with all sides equal."