Congruent — Grade 8 Math, what it means and where it is taught
Same size and same shape. Written △ ABC ≅ △ DEF.
Taught in Grade 8 Math.
Where it is taught
What uses it later
This idea is needed for:
- CPCTC — Corresponding Parts of Congruent Triangles are Congruent — used after proving congruence.
- Reflexive property — Anything is congruent to itself. A shared side is congruent to itself.
- Rhombus — A parallelogram with four congruent sides.
- AA similarity — Two pairs of congruent angles prove two triangles similar.
- SAS similarity — Two pairs of sides in ratio with the included angles congruent.
Practise this idea
26 questions in the course bank use Congruent, in Translations, Reflections & Rotations, Congruence & Sequences of Transformations, Definitions, Postulates & Reasoning, How to Write a Proof, Triangle Congruence Proofs, Quadrilaterals & Polygon Properties. The first 8 are below; the rest are in those units.
Problem 1
A figure is moved so that every point travels 6 units right and 0 units vertically. Which is true of the image?
- It is congruent to the original
- It is larger than the original
- It is a mirror image of the original
- It has different angle measures
Worked answer
It is congruent to the original
A translation changes position only
Lengths and angles are unchanged
So the image is congruent
Problem 2
Which sequence guarantees the image is congruent to the original?
- Reflect, then translate
- Dilate by 2, then translate
- Reflect, then dilate by 3
- Dilate by 12, then rotate
Worked answer
Reflect, then translate
Reflections and translations are both rigid
Dilations are not, unless k = 1
So the first sequence is the only one
Problem 3
Is AB = CD written correctly? Answer yes or no.
Worked answer
no
Segments use ≅, numbers use =.
It should be AB ≅ CD or AB = CD.
Problem 4
You know M is the midpoint of AB. What reason lets you write AM = MB?
Worked answer
definition of midpoint
A midpoint cuts a segment into two congruent parts.
That is the definition.
Problem 5
Is the converse of "if two angles are vertical, they are congruent" true? Answer yes or no.
Worked answer
no
Converse: if two angles are congruent, they are vertical.
The base angles of an isosceles triangle are congruent but not vertical.
So the converse is false.
Problem 6
In a proof, two triangles share a side. What reason lets you say that side is congruent to itself?
Worked answer
reflexive property
BD ≅ BD
That is the reflexive property.
Problem 7
CPCTC may be used
- only after proving two triangles congruent
- at any point in a proof
- to prove triangles congruent
- only in coordinate proofs
Worked answer
only after proving two triangles congruent
It is what congruence gives you.
Using it to prove congruence would be circular.
Problem 8
You are given that AB ∥ CD. What angle relationship does a transversal give you?
Worked answer
congruent alternate interior angles
Alternate interior angles are congruent.
Corresponding angles are congruent too.