Congruent Triangles Applications

Can you provide an example of how the AA similarity theorem is used to solve a problem?

• Using the Pythagorean theorem to find the measures of the corresponding sides

• Applying the Law of Sines to determine the unknown angles

• Using the AA similarity theorem to find the area of the triangles

• Identifying congruent angles in two triangles and using the proportionality of corresponding sides to solve for unknown measures.

What are the conditions for the AA similarity theorem to be applicable?

• The triangles have equal side lengths

• The triangles have a common vertex

• The triangles are both equilateral

• Two angles of one triangle are congruent to two angles of another triangle.

What are the practical applications of the AA similarity theorem?

• Calculating the area of a circle

• Solving equations in algebra

• The practical applications of the AA similarity theorem include solving problems in geometry, such as determining the similarity of two triangles and finding unknown side lengths or angles.

• Determining the boiling point of a substance

Which angle corresponds with ∠X?

• ∠N

• ∠W

• ∠E

• ∠Y

If ∆LMK ≅ ∆LMT, then ∠K ≅ (a)  

• T

• ∠T

• ∠M

• ∠L

Are the following similar? Why or why not?

• Yes. All pairs of corresponding angles are congruent.

• No, the corresponding angles are not equal.

• No, the ratios of the corresponding sides are not equal.

Are these triangles congruent?

• Yes, by ASA

• Yes, by SAS

• Yes, by AAS

• No, this is the SSA one!!

Are these triangles congruent?

• Yes, by AAS

• Yes, by SAS

• Yes, by ASA

• No, this is the SSA one!!

Are these triangles congruent?

• Yes, by AAS

• Yes, by SAS

• Yes, by ASA

• No, this is the SSA one!!

Are these triangles congruent?

• Yes, by SAS

• Yes, by AAS

• Yes, by HL

• No, this is the SSA one!!