Common Core: High School - Geometry : Congruence
Study concepts, example questions & explanations for Common Core: High School - Geometry
All Common Core: High School - Geometry Resources
Example Questions
Example Question #1 : Triangle Proofs
Which of the following theorems prove that the following two triangles are congruent?
Angle-Angle-Side Theorem
Side-Side-Side Theorem
Angle-Side-Angle Theorem
Side-Angle-Side Theorem
Side-Side-Side Theorem
These two triangles share three corresponding congruent sides. The Side-Side-Side Theorem (SSS) states that if the three sides of one triangle are congruent to their corresponding sides of another triangle, then these two triangles are congruent.
Example Question #2 : Triangle Proofs
Which of the following pairs of triangles are congruent by the ASA Theorem?
The Angle-Side-Angle Theorem (ASA) states that if two angles and their included side are congruent to two angles and their included side to another triangle, then these two triangles are congruent. Our first option cannot be correct because this figure does not give any information about the angles. This could be proven using the SSS Theorem. The second figure only gives information about one angle, this could be proven using the SAS Theorem. The third option again only gives information about one angle. The fourth figure has two angles congruent, and their included side congruent. Clearly this is the only figure that could have congruent triangles proven through the ASA Theorem.
Example Question #2 : Triangle Proofs
Which of the following theorems would prove that the following two triangles are similar?
AA Theorem
There is not enough information to determine these triangles are similar.
SAS Theorem
SSS Theorem
AA Theorem
When we look at this figure we see that we have two pairs of congruent corresponding angles, 
Example Question #3 : Triangle Proofs
Are the following two triangles similar? If so, which theorem proves this to be true?
No, these triangles are not similar
There is not enough information to determine if these triangles are similar or not
Yes, these triangles are similar by the AA Similarity Theorem
Yes, these triangles are similar by the SSS Similarity Theorem
Yes, these triangles are similar by the SSS Similarity Theorem
The Side-Side-Side Similarity Theorem states that if all three sides of one triangle are proportional to another, then these triangles are similar. 
Example Question #4 : Triangle Proofs
True or False: Side-Side-Angle is a proven theorem to prove triangle congruence.
True
False
False
Just because a triangle has two sides and one angle congruent to the two sides and angle of another triangle does not guarantee these two triangles’ congruence. For the two triangles to be congruent, the two sides that are congruent must contain the congruent angle as well. Below are two triangles that share congruent sides and one angle, but are not congruent.
Example Question #5 : Triangle Proofs
Prove that the parallelogram 
Example Question #6 : Triangle Proofs
Assume that 
Example Question #7 : 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 two pairs of congruent angles, then these two triangles are similar
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 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 #8 : Triangle Proofs
Consider triangle 
Proof:
Proof:
Proof:
Proof:
Example Question #13 : Prove Parallelogram Theorems: Ccss.Math.Content.Hsg Co.C.11
Which of the following is the definition of a parallelogram?
A quadrilateral with two pairs of opposite parallel sides
A quadrilateral with one pair of parallel sides
A quadrilateral with four right angles
A quadrilateral with four congruent sides and four congruent angles
A quadrilateral with two pairs of opposite parallel sides
A parallelogram is a quadrilateral with two pairs of opposite parallel sides such as the following.
Opposite sides of a parallelogram are congruent as well as its opposite angles.
All Common Core: High School - Geometry Resources
