19. Which of the following refers to ASA Congruence Postulate? a. The three angles of one triangle are congruent to the three angles of the second triangle. b. Two sides and an inc... 19. Which of the following refers to ASA Congruence Postulate? a. The three angles of one triangle are congruent to the three angles of the second triangle. b. Two sides and an included angle of one triangle are congruent to two sides and an included angle of the second triangle. c. Two angles and the included side of one triangle are congruent to two angles and the included side of the second triangle. d. Two angles and a non-included side of one triangle are congruent to two angles and a non-included side of the second triangle. 20. Which of the following illustration represents ASA congruence postulate? [Image of 4 triangles] 21. Which of the following illustration represents SAS congruence postulate? [Image of 4 quadrilaterals] 22. In the figure triangle POG is congruent to triangle SOR, what is the side corresponding to PO? [Image of intersecting triangles] a. OS b. RO c. RS d. SO
Understand the Problem
The image contains multiple-choice geometry questions related to triangle congruence postulates (ASA and SAS) and corresponding sides in congruent triangles. Question 19 asks for the definition of the ASA postulate. Question 20 asks to identify the figure that represents ASA congruence postulate. Question 21 asks to identify the figure that represents SAS congruence postulate. Question 22 asks to find the corresponding side to PO, given that triangle POG is congruent to triangle SOR.
Answer
19. c 22. d
Answer for screen readers
- c. Two angles and the included side of one triangle are congruent to two angles and the included side of the second triangle.
- d. SO
Steps to Solve
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Identify ASA Congruence Postulate
The Angle-Side-Angle (ASA) Congruence Postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. -
Select the Correct Option for Question 19
Based on the definition above, the correct answer for question 19 is:
c. Two angles and the included side of one triangle are congruent to two angles and the included side of the second triangle. -
Analyze Diagrams for Questions 20 and 21
To accurately choose the diagrams that represent the ASA and SAS postulates, look for elements that illustrate angles and sides properly.- For ASA, the diagram must show two angles and the side between them.
- For SAS, look for two sides and the angle between them.
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Corresponding Sides in Congruent Triangles for Question 22
In question 22, we have $\triangle POG \cong \triangle SOR$. Here, we need to find the side corresponding to $\overline{PO}$.
The correspondence is generally as follows:
- ( P \rightarrow S )
- ( O \rightarrow O ) (same point)
- ( G \rightarrow R )
Thus, side ( \overline{PO} ) corresponds to side ( \overline{SO} ).
- c. Two angles and the included side of one triangle are congruent to two angles and the included side of the second triangle.
- d. SO
More Information
The ASA postulate is a pivotal concept in geometry that helps establish triangle congruence. Understanding the relationships between angles and sides is crucial for solving various geometric problems.
Tips
- Confusing ASA with AAS (Angle-Angle-Side) or SAS (Side-Angle-Side) can lead to choosing the wrong definition.
- Misidentifying the included angle or sides in the illustrations can result in incorrectly selecting the diagrams.
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