I would like to understand to do these questions and the theorums behind them. Just an explanation and 1 example will suffice, no need to answer them all. **Do You UNDERSTAND?**1. **ESSENTIAL QUESTION** Which theorems can be used to prove two overlapping triangles are congruent?2. **Construct Arguments** How could you prove that $ \triangle ACD \cong \triangle ECB $? Diagram: Two overlapping triangles $ \triangle ACD $ and $ \triangle ECB $ sharing vertex $ C $.3. **Error Analysis** Nicholas wrote a proof to show that $ \triangle EFD \cong \triangle DGE $. Explain Nicholas's error. Is it possible to prove the triangles congruent? Explain. Diagram: Two triangles $ \triangle EFD $ and $ \triangle DGE $. _Note: The error is marked with a large "X" and indicates incorrect assumption about congruence._4. **Use Structure** Quadrilateral $ JKLM $ is a rectangle. Which triangles are congruent to $ \triangle JKL $? Explain. Diagram: A rectangle $ JKLM $ with diagonal lines, forming triangles.---**Do You KNOW HOW?**5. What are the corresponding sides and angles in $ \triangle WXV $ and $ \triangle XWY $? Diagram: Two overlapping triangles $ \triangle WXV $ and $ \triangle XWY $ sharing sides.In Exercises 6-9, name a side or angle congruent to each given side or angle.6. $ \overline{CD}A $ Diagram: Triangle featuring angles labeled A, B, C, D, E.7. $ \overline{DB} $8. $ \angle FGH $ Diagram: Triangle with vertices F, G, H, and diagonal line.9. $ \overline{HJ} $ Diagram: Triangle with vertices F, H, J.For Exercises 10 and 11, name a theorem that can be used to prove that each pair of triangles is congruent.10. $ \triangle GIL $ and $ \triangle KHL $ Diagram: Overlapping triangles sharing a side.11. $ \triangle NQM $ and $ \triangle PMQ $ Diagram: Overlapping triangles sharing a vertex and a side.---**Topic 4: Triangle Congruence**Illustrations aid in understanding of triangle congruence through constructions and theorems, offering exercises

Name: I would like to understand to do these questions and the theorums behi
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Description: I would like to understand to do these questions and the theorums behind them. Just an explanation and 1 example will suffice, no need to answer them all. **Do You UNDERSTAND?**1. **ESSENTIAL QUESTION** Which theorems can be used to prove two overlap

Given :- Theorems required to prove two overlapping triangles are congruent. SOLUTION :- To prove the two overlapping triangles are congruent , we use the following criterion SSS Theorem SAS theorem ASA theorem AAS theorem HL theorem Two triangles are said to be congruent if their corresponding sides are equal in length and their corresponding interior angles are equal in measure. Here , corresponding sides and angles means that the side of one triangle and the side of the other triangle are in the same position. SSS Theorem :- The SSS means side side side postulate means triangles are congruent to the corresponding sides of the other triangle. SAS Theorem :- The SAS means side angle side postulate says that the triangles are congruent if any pair of corresponding sides and their included angles are congruent. ASA Theorem :- The ASA means angle side angle postulate says that the triangles are congruent if any two angles and their included angles are equal in the triangles. An included side is the side between two angles. AAS Theorem :- The AAS means angle angle side postulate says that the two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle , the triangles are congruent. Here , non-included means that take two consecutive angles and then move on to the next side in either direction. HL Theorem :- The HL means Hypotenuse leg states that if the hypotenuse and one leg of a right angle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent. EXAMPLE :- The two triangles are next to each other and they share a common side, AC. Since AC is the same side in both triangles, we know that it must be congruent to itself. This property is called the reflexive property of congruence, which says that any segment or angle is congruent to itself. Hence, by SSS congruent property. Hence, these are the theorems required to solve all these questions.

Answered: ESSENTIAL QUESTION Which theorems can…

Math

Advanced Math

ESSENTIAL QUESTION Which theorems can be used to prove two overlapping triangles are congruent?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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