Similarity Proving
In this lesson, you will learn how to prove that two triangles are similar by using AA Similarity or ratio of length of sides.
Related Lessons:
Proving Similarity
The most common method to prove similarity is the AA Similarity method, where you show that two corresponding angles are equal. Once two angles are equal, the third angle will obviously be equal because the angles in a triangle add up to 180°.
In some schools, you may be required to state AAA Similarity, where all three angles are shown to be equal. Be sure to check with your teacher on the required method.
In some questions, AA Similarity cannot be proven. Then you may need to prove using ratio of sides are equal. There are two possible scenarios:
- Prove all three corresponding sides have equal ratio
- Prove two corresponding sides have equal ratio, and one pair of angles are equal
Proving Similarity Example 1
ABC is a triangle with points X and Y on AB and AC respectively. AX=4cm, XB=28cm, XY=6cm and AY=YC=8cm.
- Show that triangles ABC and AYX are similar.
- Find the length of BC.
Proving Similarity Example 2
In the diagram, ∠𝑃𝑄𝑋=∠𝑄𝑅𝑋. Given that PQ=12cm, PR=18cm and QX=10cm,
- Write down a pair of similar triangles, indicating the reasons for their similarity
- Hence find the length of PX.