Proving Triangles Similar

Proving Triangles Similar

You should familiarize yourself with this content, but we are looking for completion for understanding

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• Corresponding Angles are CONGRUENT

• Corresponding Sides are PROPORTIONAL

​Similar Shapes are the result of a dilation

Criteria for Similar Shapes

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Multiple Choice

Which of the below is the only correct similarity statement for the two triangles?

• $$\Delta SKE\sim\Delta THC$$  

• $$\Delta SKE\sim\Delta TCH$$  

• $$\Delta SKE\sim\Delta CHT$$  

• $$\Delta SKE\sim\Delta HCT$$  

Multiple Choice

The quadrilateral ABCD is dilated using the center point A to create quadrilateral AEFG. Determine the length of segment DC given the measurements provided in the figure.

• $$5$$  

• $$8.333$$  

• $$7.5$$  

• $$7.6666$$  

If two angles of one triangle are congruent to the corresponding angles of another triangle, the triangles are similar.

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​​Angle Angle Similarity Theorem (AA):

Multiple Select

Which of these triangle pairs can be proven similar using AA? Mark all that apply.

If the three sets of corresponding sides of two triangles are in proportion, the triangles are similar.

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Side-Side-Side Similarity Theorem (SSS):

Multiple Select

Identify which triangles can be proven similar using the SSS Theorem. Mark all that apply.

Multiple Choice

Can you prove the triangles similar by SSS Theorem?

• Yes--the sides are all proportional.

• No--there is not enough information provided for SSS

If an angle of one triangle is congruent to the corresponding angle of another triangle and the lengths of the sides including these angles are in proportion, the triangles are similar.

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Side-Angle-Side Similarity Theorem (SAS):

Multiple Choice

Can you prove the triangles similar by SAS Theorem?

• Yes--the corresponding sides are proportional and the included angle is a vertical angle so it is congruent.

• No--there is not enough information provided for SAS

Multiple Choice

Identify which of the following triangles are similar by SAS Theorem.

Multiple Choice

Using (SSS, AA, SAS) can you determine must be similar? If so, explain why.

• Yes, by SSS

• Yes, by AA

• Yes, by SAS

• There is not enough information to prove similarity

Multiple Choice

Using (SSS, AA, SAS) can you determine must be similar? If so, explain why.

• Yes, by SSS

• Yes, by AA

• Yes, by SAS

• There is not enough information to prove similarity

Multiple Choice

Using (SSS, AA, SAS) can you determine must be similar? If so, explain why.

• Yes, by SSS

• Yes, by AA

• Yes, by SAS

• There is not enough information to prove similarity

Multiple Choice

Using (SSS, AA, SAS) can you determine must be similar? If so, explain why.

• Yes, by SSS

• Yes, by AA

• Yes, by SAS

• There is not enough information to prove similarity

Multiple Choice

Using (SSS, AA, SAS) can you determine must be similar? If so, explain why.

• Yes, by SSS

• Yes, by AA

• Yes, by SAS

• There is not enough information to prove similarity