https://www.basic-mathematics.com/geometry-proofs.html

The formula to find the area of a circle is

A = π × r²

PROOF

area of triangle ABC = area of triangle ABE + area of triangle CBE

area of triangle ABC = (y × h)/2 + (x × h)/2

area of triangle ABC = (y × h + x × h)/2

area of triangle ABC = h ×(y + x)/2

Notice that y + x is the length of the base of triangle ABC.

Thus, it is ok to say that y + x = b

Therefore, area of triangle ABC = (h × b)/2

PROOF

1. Draw a parallelogram.
2. Cut a right triangle from the parallelogram. 
3. Use the right triangle to turn the parallelogram into a rectangle.
4. The parallelogram will have the same area as the rectangle you created that is b × h

PROOF

PROOF

Our 'tradie' narrator is busy constructing a playground. Follow along as she goes beyond practical demonstrations to mathematically prove that she is creating sunshade shapes that are congruent or similar to the equipment they are covering. By applying logical reasoning, she is able to work through her proofs step by step.

Our narrator is planning the layout of a new playground; she needs to recognise properties that determine congruence and which transformations create congruent figures. Follow along as she determines whether two figures are congruent after transformations (translation, reflection, rotation).

Two triangles are congruent if they have:

• exactly the same three sides and
• exactly the same three angles.

But we don't have to know all three sides and all three angles ...usually three out of the six is enough.

There are five ways to find if two triangles are congruent: SSS, SAS, ASA, AAS and HL.

READ MORE

How To Find if Triangles are Congruent. (n.d.). Retrieved from https://www.mathsisfun.com/geometry/triangles-cong ruent-finding.html

Two triangles are similar if they have:

• all their angles equal
• corresponding sides are in the same ratio

But we don't need to know all three sides and all three angles ...two or three out of the six is usually enough.

There are three ways to find if two triangles are similar: AA, SAS and SSS

READ MORE

How To Find if Triangles are Similar. (n.d.). Retrieved from https://www.mathsisfun.com/geometry/triangles-simi lar-finding.html

Segment AB ≅ segment CD and segment BC ≅ AD

PROOF

Segment AC ≅ segment BD

PROOF

segment AC ≅ segment BD

PROOF

Prove m ∠ a = m ∠b

Note that m ∠ a means measure of angle a

PROOF

Note in the window below you can move points A, B, C, and D.