Question 1
Identify the two congruent shapes from the options below:
Select the correct answer from the list below:
A: C and D
B: D and F
C: G and C
D: A and E
CORRECT ANSWER: D: A and E
WORKED SOLUTION:
If we rotate A 90^\circ clockwise, then it will fit perfectly over E.
Question 2
Identify the two congruent shapes from the options below:
Select the correct answer from the list below:
A: B and E
B: D and G
C: C and F
D: D and E
CORRECT ANSWER: A: B and E
WORKED SOLUTION:
If we rotate B or E 180^\circ then they will fit perfectly over the other.
Question 3
If the following two triangles are congruent, what information is missing on the second triangle to prove this?
Select the correct answer from the list below:
A: x=60^\circ
B: y=60^\circ
C: No more information required to prove congruence.
D: Impossible for the triangles to be congruent.
CORRECT ANSWER:A: x=60^\circ
WORKED SOLUTION:
In our original triangle we only have Side-Angle-Side, so for the two triangles to be congruent we have to use this same rule, meaning that the angles between the two sides have to be the same. This gives us x=60^\circ
Question 4
Which, if any, of the triangles labelled A, B, or C, is congruent to the triangle labelled X?
Select the correct answer from the list below:
A: A
B: B
C: C
D: None of these are congruent
CORRECT ANSWER: B: B
WORKED SOLUTION:
Although A has 55^\circ surrounded by two sides, like X, these sides are different. A is not congruent to X.
B has all the same sides as X so, using the Side-Side-Side (SSS) rule, we can say that B is congruent to X.
C doesn’t have enough information to determine congruence, we need at least three pieces of information.
Question 5
Which, if any, of the triangles labelled A, B, or C, is congruent to the triangle labelled X?
Select the correct answer from the list below:
A: A
B: B
C: C
D: None of these are congruent.
CORRECT ANSWER: C: C
WORKED SOLUTION:
A only has two sides that are the same as X, so they are not congruent.
Although X and B have all of the same angles, this isn’t enough to determine congruence.
X and C both have the same angles separate by the same length side. We can use Angle-Side-Angle to determent that X and C are congruent.