Triangles Test

Result

Triangles Test - 5

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Weekly Quiz Competition

Question 1
1 / -0

What is the name of the congruence rule which proves the congruency of two triangles using the right angle?

A
SSA

B
HL

C
ASA

D
SAS

Solution

If the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the two right triangles are congruent. Therefore, HL congruency rule will be used to prove that two right-angled triangles are congruent.
Question 2
1 / -0

Fill in the blanks:

I. The sum of any two sides of a triangle is __P__ than the third side.
II. In triangles PQR and FJK, if PQ = FJ, PR = FK and QR = JK, then ΔPQR ≅ ΔFJK by ___Q___ congruency rule.
III. According to a property of triangles, the side opposite to the __R__ angle is the shortest side of the triangle.

A
P - greater, Q - SAS, R - smallest

B
P - greater, Q - SSS, R - smallest

C
P - greater, Q - ASA, R - largest

D
P - smaller, Q - SAS, R - largest

Solution

I. The sum of any two sides of a triangle is greater than the third side.
II. In triangles PQR and FJK, if PQ = FJ, PR = FK and QR = JK, then ΔPQR ≅ ΔFJK by SSS congruency rule.
III. According to a property of triangles, the side opposite to the smallest angle is the shortest side of the triangle.
Question 3
1 / -0

Which of the following is the CORRECT statement?

A
If the three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent by ASA rule.

B
The reflexive property of congruence shows that all geometric figures are congruent to each other.

C
AAA congruence rule does not work when we have to determine if two triangles are congruent because it can produce similar but not congruent triangles.

D
If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent by SSS congruence rule.

Solution

1. If three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent by ASA rule. (INCORRECT) This is true by SSS rule.

2. The reflexive property of congruence shows that all geometric figures are congruent to each other. (INCORRECT) The reflexive property of congruence shows that any
geometric figure is congruent to itself.

3. AAA congruence rule does not work when we have to determine if two triangles are congruent because it can produce similar but not congruent triangles. (CORRECT)

4. If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent by SSS congruence rule. (INCORRECT) This is true by SAS congruence rule.