Prove triangle PQS is similar to triangle QRS

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In summary, to prove that two triangles are similar, it must be shown that they have the same shape and angles, but may differ in size. This can be done by demonstrating that their corresponding angles are congruent and their corresponding sides are in proportion. Congruent triangles are identical in shape and size, while similar triangles have the same shape but may differ in size. Two triangles are similar if they have the same shape and their corresponding angles are congruent, and their corresponding sides are in proportion. The SAS similarity theorem can be used to prove that two triangles are similar by showing that they have two pairs of corresponding sides that are proportional and an included angle that is congruent. Proving that two triangles are similar is important as it allows
  • #1
aricho
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I'm having trouble doing this...

prove triangle PQS is similar to triangle QRS
Hence prove QS^2=PS.SR

the diagram is attached

cheers
 

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  • #2
Look at the angles. angles QPS and QRS are complementary. So are QQS and PQS.
 
  • #3
yer, but how can u prove that they triangles are similar?
 
  • #4
If two triangles contain the same three angles, then they are similar.
 

1. How do you prove that two triangles are similar?

To prove that two triangles are similar, you must demonstrate that they have the same shape and angles, but may differ in size. This can be done by showing that their corresponding angles are congruent and their corresponding sides are in proportion.

2. What is the difference between congruent and similar triangles?

Congruent triangles are identical in shape and size, while similar triangles have the same shape but may differ in size. Congruent triangles have corresponding angles and sides that are equal, while similar triangles have corresponding angles that are congruent and corresponding sides that are in proportion.

3. What are the conditions for two triangles to be similar?

Two triangles are similar if they have the same shape and their corresponding angles are congruent. Additionally, their corresponding sides must be in proportion, meaning that the ratio of any two corresponding sides is equal.

4. How can you prove that two triangles are similar using the Side-Angle-Side (SAS) similarity theorem?

The SAS similarity theorem states that if two triangles have two pairs of corresponding sides that are proportional and an included angle that is congruent, then the triangles are similar. This can be proven by setting up a proportion with the corresponding sides and using the Angle-Angle (AA) similarity theorem to show that the remaining angles are congruent.

5. What is the importance of proving that two triangles are similar?

Proving that two triangles are similar is important because it allows us to make accurate predictions and calculations about the relationship between their corresponding angles and sides. This can be applied in various fields such as engineering, architecture, and geometry to solve real-world problems and design structures that are stable and functional.

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