Common Core: High School - Geometry : Prove Triangle Theorems: CCSS.Math.Content.HSG-CO.C.10
Study concepts, example questions & explanations for Common Core: High School - Geometry
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Example Questions
Example Question #1 : Triangle Proofs
Which of the following describes the Angle-Side-Angle Similarity Theorem?
If two triangles have two pairs of sides are of the same proportions and their included angles are congruent, then these two triangles are congruent
If two triangles share all three pairs of sides in the same proportions, then these two triangles are similar
If two triangles have two pairs of sides are of the same proportions and their included angles are congruent, then these two triangles are similar
If two triangles share two pairs of congruent angles, then these two triangles are similar
If two triangles have two pairs of sides are of the same proportions and their included angles are congruent, then these two triangles are similar
The Angle-Side-Angle Similarity Theorem states that if two triangles have two pairs of sides are of the same proportions and their included angles are congruent, then these two triangles are similar. To be similar triangles can be different sizes, but all angles must be congruent. If two triangles have a pair of congruent angles, then we know their opposite side of that angle must be in proportion to each other. If we also have two pairs of sides that are of the same proportions then these triangles would be similar. This theorem guarantees these conditions are met.
Example Question #3 : Triangle Proofs
Consider triangle 
Proof:
Proof:
Proof:
Proof:
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