Triangle Congruence (ASA, SAS, SSS)
Using Rigid Motions to Prove Congruence
Lines and Angles Theorems
Mixed Geometry Challenge
Reflexive Property
100
This congruence criterion proves two triangles are congruent when two angles and the included side match.
What is ASA?
100
A transformation that slides a shape without turning it.
What is a translation?
100
Angles directly across from each other when two lines intersect.
What are vertical angles?
100
A transformation that keeps the shape congruent and in the same orientation.
What is a translation?
100
The reflexive property states that any geometric object is always equal to this.
What is Itself.
200
This congruence criterion requires two sides and the included angle to be equal.
What is SAS?
200
A transformation that turns a figure around a fixed point.
What is a rotation?
200
When parallel lines are cut by a transversal, these angles are equal and are found in the same relative position.
What are corresponding angles?
200
If two angles form a straight line, they are this type of angle pair.
What are supplementary angles?
200
The reflexive property is most commonly used in triangle congruence proofs when triangles share this.
What is A common side?
300
If all corresponding sides of two triangles are equal, they are congruent by this postulate.
What is SSS?
300
The transformation that flips a figure over a line.
What is a reflection?
300
Angles on opposite sides of the transversal but inside the parallel lines.
What are alternate interior angles?
300
Triangles proven congruent by SSS must have all of these equal.
What are corresponding side lengths?
300
In a congruence proof, saying AB ≅ AB is an example of which property?
What is The reflexive property of equality?
400
A rigid motion that can show two triangles are congruent because it preserves both side lengths and angles.
What is a reflection, rotation, or translation?
400
Rigid motions preserve these two properties.
What are distance and angle measure?
400
This theorem states that vertical angles are…
What is congruent?
400
When completing this two column proof what would be your first step?
What is write down what you are given?
400
When two triangles share a side, the reflexive property helps prove which congruence criterion that includes a shared side?
What is SAS (Side-Angle-Side).
500
If triangle ABC can be mapped onto triangle DEF using two rigid motions, then these triangles share this geometric property.
What is congruence?
500
If triangle ABC is rotated 90° about the origin to match triangle A′B′C′, what is true about the two triangles?
What is they are congruent?
500
A proven statement that if two lines are cut by a transversal and same-side interior angles are supplementary, then the lines must be this.
What is parallel?
500
You are proving that △ABC ≅ △DEF. You know that AB ≅ DE and BC ≅ EF, but you do not know angle measures.
You construct a perpendicular bisector of segment AD, showing that point B and point E both lie on this bisector.
Which triangle congruence theorem does this construction allow you to use to complete the proof?
What is SSS (Side-Side-Side) Congruence?
500
In a proof involving triangles △ABD and △CBD, students often use the reflexive property to justify that BD ≅ BD.
What key role does this reflexive statement play in establishing triangle congruence when combined with two pairs of corresponding sides?
What is providing the third side needed to apply SSS Congruence?