1. with Selected Review Questions from Previous Material
Chapter 4 Test Review
Congruent Triangles
with Selected Review Questions from Previous Material

2. Congruent Triangles Review
BOTH Brain Dumps are on the test!!
REMEMBER:
CPCTC!!
Corresponding Parts of Congruent Triangles are Congruent.
Reflexive sides are congruent to themselves.
Vertical Angles are always congruent.

3. Congruent Triangles Review
There are FIVE (5) ways to prove that triangles are congruent.
1) SSS – Side, Side, Side: All three sides of one triangle have a corresponding, congruent side in the other triangle.
2) SAS – Side, Angle, Side: The congruent parts of the triangles include two sides, with the angle that is between them.
3) ASA – Angle, Side, Angle: The congruent parts of the triangles include two angles, with the side that is between them.
4) AAS – Angle, Angle, Side: The congruent parts of the triangles include two angles, with a side that is NOT between them.
5) HL – Only applies to RIGHT triangles. If the hypotenuse and one other leg are congruent, the triangles are congruent.

4. Reason (Justification)
Geometry – 2 Column Proofs
Put WHAT you know in the left hand column.
Put WHY or HOW you know it in the right hand column.
Given: 𝐴𝐸 and 𝐶𝐷 bisect each other
Prove: ∆𝐴𝐵𝐶≅∆𝐸𝐵𝐷 A B C D E
Statement
Reason (Justification)
𝐴𝐵 ≅ 𝐵𝐸
Definition of bisector
𝐶𝐵 ≅ 𝐵𝐷
Definition of bisector
∠𝑎𝑏𝑐≅∠𝑑𝑏𝑒
Vertical Angles are congruent
∆𝐴𝐵𝐶≅∆𝐸𝐵𝐷
SAS
The “Prove” statement is ALWAYS last!!!

5. Given
Vertical Angles are congruent
∆𝑌𝐴𝑍≅∆𝐵𝐴𝐶
ASA
𝐴𝑍 ≅ 𝐴𝐶
CPCTC

6. Congruency Review EXAMPLES:
We know about CPCTC, so we just need to find the corresponding parts and fill in our polygon. We can solve for x from there.
Since angle Q and angle L correspond, angle L is also 45 degrees.
R and M correspond, so M is 3x.
We know from our Brain Dump that the interior angles of a polygon add up to (n – 2)180, so these polygons add up to (4 – 2) 180, or (2)180, or 360.
There are 360 degrees in these polygons.

7. Congruency Review EXAMPLES: 45 + 3x + x + 5x = 360 9x + 45 = 360

8. Congruency Review EXAMPLES: Find the value of x:
Mark what we can tell from the picture.
𝐶𝐷 ≅ 𝐴𝐵 (they are both 4.7 units in length)
𝐴𝐶 ≅ 𝐵𝐷 (they are both 3.4 units in length)
𝐶𝐵 ≅ 𝐶𝐵 (Reflexive side)
Based on this, we know that ∆𝐶𝐴𝐵≅∆𝐵𝐷𝐶 (SSS)
From here, we can see that ∠𝑑𝑐𝑏≅∠𝑎𝑏𝑐 (CPCTC)
That means that x = 320.

9. Reason (Justification)
Congruency Review
EXAMPLES:
Let’s begin by marking what we know and filling in the table.
Statement
Reason (Justification)
∠𝐵≅∠𝐷
Definition of Right Angles
𝐵𝐶 ≅ 𝐶𝐷
Definition of bisector
∠𝑏𝑐𝑎≅∠𝑒𝑐𝑑
Vertical Angles are congruent
∆𝐴𝐵𝐶≅∆𝐸𝐷𝐶
ASA

10. Congruency Review x0 EXAMPLES: Solve for x and y:
We have to do some thinking and applying prior knowledge here, but the process is pretty straight-forward.
Because the two bottom angles are opposite equal sides, they must be equal.
They both equal x degrees. x0

11. Congruency Review x0 EXAMPLES: Solve for x and y:
We also know that the 1350 angle and the x are linear, which makes them supplementary.
135 + x = 180
x = 45.
We have 2 angles of 450, so the third angle must be 900 (they add to 180)
y = 900 x0

12. Congruency Review EXAMPLES:
What additional information is needed to prove that ∆𝐷𝐴𝐸 ≅∆𝑅𝑄𝑆 using the HL Law?
We need to know that angle A and angle Q are right angles.

13. Other Skills to Remember (Review from Previous Units)
ALL OF THESE ARE PART OF THE CYCLE 1 BRAIN DUMP!!!
1) Find the missing endpoint of a line segment when given one endpoint and the midpoint.
2) Find the sum of the interior angles of any polygon.
3) Know the definition of a regular polygon.
4) Know and be able to use the distance formula, especially when given two endpoints.
5) Be able to find the midpoint of a segment when given the endpoints.