Q.No.6. Take the cut-outs of the following pairs of triangles and observe if the pairs are congruent? (1) Two triangles having all three corresponding pairs of angles equal. (ll) Two triangles having only two corresponding pairs of angles equal.
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Given: the cut-outs of the two pairs of triangles and observe if the pairs are congruent
The answer is "1".
Two triangles having all three corresponding pairs of angles equal.
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Step-by-step explanation:
- Given: Cutouts of Following Pairs of Triangles: i) Two triangles having all three corresponding pairs of angles equal.
ii) Two triangles having only two corresponding pairs of angles equal.
- To Find: If the pairs are congruent or not.
- We know, In geometry, two figures or objects are said to be congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other. They will be perfectly aligned.
- Here, We are given that the triangles have all three corresponding pairs of angles equal, but we are not given any information about the sides of the triangles which determine its size. So, these triangle won't at all be congruent.
Therefore, Two triangles having all three corresponding pairs of angles equal won't necessarily be congruent.
- Secondly, we are given that Two triangles having only two corresponding pairs of angles equal. We know by angle sum property of triangles that if Two triangles having only two corresponding pairs of angles equal, then the third pair will also be equal. So, we can again apply the same knowledge of congruency as above where size is undetermined.
Therefore, Two triangles having only two corresponding pairs of angles equal won't necessarily be congruent.
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