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:

Step1: Recall properties of congruent - shapes

Congruent shapes have all corresponding sides and angles equal. For quadrilaterals, rectangles, and rhombuses, having one - side length equal is not sufficient for congruence.

Step2: Analyze squares

Squares have all sides equal. If one side of a square has a length of 3 units, then all sides have a length of 3 units. By the Side - Side - Side (SSS) congruence criterion for polygons, all squares with at least one side length of 3 units are congruent.

Step3: Recall triangle congruence criteria

The Side - Angle - Side (SAS) criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, the triangles are congruent. The Angle - Side - Angle (ASA) criterion states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent. The Side - Side - Side (SSS) criterion states that if three pairs of congruent sides exist in two triangles, the triangles are congruent.

Step4: Match statements with triangle diagrams

For the first triangle diagram, we have two sides and the included angle marked as congruent, which is SAS. For the second triangle diagram, we have two angles and the included side marked as congruent, which is ASA. For the third triangle diagram, we have three pairs of congruent sides marked, which is SSS.

Answer:

1. D. All squares with at least one side length of 3 units are congruent.
2. A - 1 (SAS), B - 2 (ASA), C - 3 (SSS)