Question

3 which conjecture is possible to prove?
a all quadrilaterals with at least one side length of 3 units are congruent.
b all rectangles with at least one side length of 3 units are congruent.
c all rhombuses with at least one side length of 3 units are congruent.
d all squares with at least one side length of 3 units are congruent.
4 from unit 2, lesson 4
match each statement using only the information shown in the pairs of
congruent triangles.
a the 2 sides and the
included angle of one
triangle are congruent to
2 sides and the included
angle of another triangle.
b the 2 angles and the
included side of one
triangle are congruent to
2 angles and the included
side of another triangle.
c in the two triangles,
there are 3 pairs of
congruent sides.

Explanation:

Question 3

Step1: Analyze option A

Quadrilaterals can have different shapes (e.g., parallelogram, trapezoid) even with a side - length of 3 units. So, they are not congruent.

Step2: Analyze option B

Rectangles can have different lengths for the other side (e.g., a rectangle with sides \(3\times4\) and \(3\times5\)). So, they are not congruent.

Step3: Analyze option C

Rhombi can have different angles (e.g., a rhombus with angles \(60^{\circ}\) and \(120^{\circ}\) and another with angles \(80^{\circ}\) and \(100^{\circ}\)) even with side - length 3. So, they are not congruent.

Step4: Analyze option D

Squares have all sides equal. If one side is 3 units, then all sides are 3 units and all angles are \(90^{\circ}\). By the SSS (Side - Side - Side) congruence criterion (for polygons, when all corresponding sides and angles are equal), all such squares are congruent.

For pair 1

We have two sides and the included angle. So, it matches with statement A.

For pair 2

We have three pairs of congruent sides. So, it matches with statement C.

For pair 3

We have two angles and the included side. So, it matches with statement B.

Answer:

D. All squares with at least one side length of 3 units are congruent.

Question 4