GCSE Secondary Maths Age 13-17 - Algebra: Cosine Rule - Explained

The video tutorial explains how to prove that line AC is equal to line BD in a quadrilateral ABCD, where AB equals CD and angle ABC equals angle BCD. The teacher separates the quadrilateral into two triangles, ABC and BCD, to demonstrate congruency using the side-angle-side condition. By proving the triangles congruent, it is concluded that AC equals BD. The tutorial also highlights the importance of identifying common elements and reviews the four conditions of congruency.

What is the initial problem statement involving quadrilateral ABCD?

• Prove that AC is equal to BD

• Prove that ABCD is a rectangle

• Prove that AB is equal to CD

• Prove that angle ABC is equal to angle BCD

Why does the speaker separate the quadrilateral into two triangles?

• To change the problem statement

• To simplify the proof process

• To prove that ABCD is a square

• To make the diagram more complex

Which condition of congruency is used to prove the triangles are congruent?

• Right Angle-Hypotenuse-Side

• Side-Angle-Side

• Angle-Side-Angle

• Side-Side-Side

What is the significance of the common side BC in the proof?

• It is irrelevant to the proof

• It helps in proving the triangles are congruent

• It shows that AC is longer than BD

• It proves that ABCD is a parallelogram

What conclusion is drawn from the congruency of the triangles?

• AB is equal to CD

• AC is longer than BD

• Angle ABC is equal to angle BCD

• AC is equal to BD

Which of the following is NOT a condition of congruency?

• Side-Angle-Side

• Side-Side-Side

• Angle-Angle-Angle

• Angle-Side-Angle

What is the easiest way to approach the problem according to the speaker?

• By using a calculator

• By assuming AC is equal to BD

• By separating the quadrilateral into two triangles

• By drawing the original diagram