Understanding Rhombus Diagonals

The video tutorial provides a proof that the diagonals of a rhombus are perpendicular. It begins by defining a rhombus and its properties, explaining that all sides are equal and some rhombuses are squares. The tutorial then focuses on the diagonals, illustrating how they form congruent triangles and discussing the role of altitudes in isosceles triangles. The proof concludes by demonstrating that the diagonals bisect each other at right angles, using geometric principles such as congruence and symmetry.

What is a rhombus?

• A square with unequal sides

• A quadrilateral with all sides equal and angles of 90 degrees

• A parallelogram with all sides equal

• A rectangle with all sides equal

Which statement is true about squares and rhombuses?

• All rhombuses are squares

• All squares are rhombuses

• No rhombuses are squares

• No squares are rhombuses

How does changing the orientation of a rhombus affect its properties?

• It changes the side lengths

• It changes the angles

• It does not change any properties

• It changes the area

What theorem is used to prove the congruence of triangles formed by a rhombus's diagonals?

• Angle-Angle-Side

• Side-Side-Side

• Side-Angle-Side

• Angle-Side-Angle

What type of triangles are formed by the diagonals of a rhombus?

• Equilateral triangles

• Isosceles triangles

• Scalene triangles

• Right triangles

What is true about the base angles of isosceles triangles in a rhombus?

• They are equal

• They are supplementary

• They are different

• They are complementary

What happens when an altitude is dropped in an isosceles triangle?

• It creates two obtuse triangles

• It creates two equilateral triangles

• It creates two congruent right triangles

• It creates two scalene triangles

What is the relationship between the diagonals of a rhombus?

• They bisect each other and are perpendicular

• They are parallel

• They are equal

• They are congruent

What does the altitude in an isosceles triangle also act as?

• A bisector

• A median

• A secant

• A tangent

What is the result of dropping an altitude from the unique vertex of an isosceles triangle?

• It creates two congruent right triangles

• It creates two scalene triangles

• It creates two obtuse triangles

• It creates two equilateral triangles