Multiple geometry questions on congruence postulates, and properties of congruent triangles.
Understand the Problem
This image contains multiple geometry questions. Question 19 asks for the definition of ASA (Angle-Side-Angle) congruence postulate. Question 20 and 21 ask which figures represent ASA and SAS postulates respectively, and question 22 deals with corresponding sides in congruent triangles given (\triangle POG \cong \triangle SOR), asking to identify the side that corresponds to (\overline{PO}).
Answer
c; d. \( SO \)
Answer for screen readers
- c
- (Select the illustration representing ASA, generally the one with two angles and an included side)
- (Select the illustration representing SAS, generally the one with two sides and an included angle)
- d. ( SO )
Steps to Solve
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Identify the ASA Congruence Postulate Definition To determine which option describes the ASA Congruence Postulate, we need to know its definition. The 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 two triangles are congruent.
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Select Correct Option for ASA Given the definitions:
- Option c: "Two angles and the included side of one triangle are congruent to two angles and the included side of the second triangle." describes ASA. Thus, the correct answer is option c.
- Assess Illustrations for ASA and SAS For question 20, we need to look at the illustrations and identify which one represents ASA:
- The figure with two angles and the side between them indicated as congruent represents ASA.
- For question 21, the illustration representing SAS must show two sides and the included angle.
- Identify Corresponding Sides in Triangles For question 22, given the congruent triangles (\triangle POG \cong \triangle SOR), we find the side corresponding to (\overline{PO}):
- From the labeling, (\overline{PO}) corresponds to (\overline{SO}) since they are on the same relative positions in their respective triangles.
- c
- (Select the illustration representing ASA, generally the one with two angles and an included side)
- (Select the illustration representing SAS, generally the one with two sides and an included angle)
- d. ( SO )
More Information
The ASA Congruence Postulate is fundamental in geometry for proving triangle congruency. Understanding triangle congruence is essential for various geometric proofs and theorems, such as those involving angles and side lengths. Illustrating these properties effectively helps in visual comprehension, making geometry clearer.
Tips
- Confusing the definitions of ASA and SAS. ASA involves two angles and the included side, while SAS involves two sides and the included angle.
- Misidentifying congruent parts in illustrations; always check for the correct arrangement of angles and sides.
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