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6 Geometric proofs

6.01 Proving triangles congruent and similar

6.02 Further triangle proofs

Stage 5.1-2

6.02 Further triangle proofs

Lesson

Worksheet

Practice

Worksheet

Further proofs for similar triangles

Consider the diagram.

How do we know $BE$ is parallel to $CD$ ?

Which angle is equal to $\angle BEA$ ?

How do we know $\triangle ABE \sim \triangle ACD$ ?

State the enlargement factor going from the smaller triangle to the larger triangle.

Find the value of the pronumeral.

Consider $\triangle ABC$ and $\triangle PQR$ :

Prove that $\triangle ABC$ is similar to $\triangle PQR$ .

Find the value of $x$ .

Find the value of $y$ .

Consider the following diagram:

Prove that $\triangle AOB$ and $\triangle DOC$ are similar.

Hence, show that $AB \parallel CD$ .

In the diagram, $QR \parallel ST$ .

Show that $\triangle PQR$ is similar to $\triangle PST$ .

Find the scale factor of enlargement.

Find the value of $f$ .

Consider the diagram below.

Prove that the $\triangle ABE$ and $\triangle ACD$ are similar.

Find the value of $f$ .

Consider the following diagram:

Prove that $\triangle ABC$ and $\triangle ADB$ are similar.

Find the length $x$ .

Consider the diagram below:

Prove that $\triangle ABE$ is similar to $\triangle BCD$ .

Prove that $\triangle EDB$ is similar to $\triangle BCD$ .

Can we conclude that $\triangle ABE$ is similar to $\triangle EDB$ ?

In the diagram, $\triangle ABC$ is a right-angled triangle with the right angle at $C$ . The midpoint of $AB$ is $M$ and $MP$ is perpendicular to $AC$ .

Prove that $\triangle AMP$ is similar to $\triangle ABC$ .

Find the ratio of $AP$ to $AC$ .

Prove that $AB$ is parallel to $CD$ for the following diagram:

Prove that $CE = EB$ for the following diagram:

Prove that $BD^{2} = AD \times DC$ for the following diagram:

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6.02 Further triangle proofs