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QUESTION IMAGE

select the statement that most accurately describes the given informati…

Question

select the statement that most accurately describes the given information between the congruent triangles. image of a quadrilateral with a diagonal, showing congruent side markings \bigcirc three sides of one triangle are congruent to three sides of another triangle. \bigcirc two angles and a non - included side of one triangle are congruent to two angles and a non - included side of another triangle. \bigcirc two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle. \bigcirc two angles and the included side of one triangle are congruent to two angles and the included side of another triangle. \bigcirc none of these statements accurately describe the given information between the triangles.

Explanation:

Step1: Analyze the diagram

The diagram shows a quadrilateral divided into two triangles by a diagonal. The markings indicate that three pairs of sides are congruent (two sides with single ticks, two sides with double ticks, and the diagonal is common). So, we are looking at the SSS (Side - Side - Side) congruence criterion.

Step2: Evaluate each option

  • Option 1: "Three sides of one triangle are congruent to three sides of another triangle." This matches the SSS criterion as we have three pairs of congruent sides (the two sides with single ticks, two sides with double ticks, and the common diagonal).
  • Option 2: Talks about two angles and a non - included side, which is AAS (Angle - Angle - Side) or SSA (Side - Side - Angle, which is not a valid congruence criterion in general). This does not match the diagram.
  • Option 3: Talks about two sides and the included angle (SAS - Side - Angle - Side). The diagram does not show any angle markings, so this is not correct.
  • Option 4: Talks about two angles and the included side (ASA - Angle - Side - Angle). Again, no angle markings in the diagram, so this is incorrect.
  • Option 5: Since option 1 is correct, this is incorrect.

Answer:

A. Three sides of one triangle are congruent to three sides of another triangle.