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Is it possible to prove that the triangles are congruent? If so, state the postulate or theorem you would use. Explain your reasoning. b. P а. E R F Solution a. The diagram shows that ZEGH and ZEGF are right angles. So, = L__. Also, of Congruence. This is triangles are congruent. by the Reflexive Property information to prove that the b. In addition to the angles that are marked, Reflexive Property of Congruence. angles and the one pair of corresponding You can use the by the of corresponding are congruent. to prove that

Is it possible to prove that the triangles are congruent? If so, state the postulate or theorem you would use. Explain your reasoning. b. P а. E R F Solution a. The diagram shows that ZEGH and ZEGF are right angles. So, = L__. Also, of Congruence. This is triangles are congruent. by the Reflexive Property information to prove that the b. In addition to the angles that are marked, Reflexive Property of Congruence. angles and the one pair of corresponding You can use the by the of corresponding are congruent. to prove that

Advanced Engineering Mathematics
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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**Example 1: Developing Proof** **Is it possible to prove that the triangles are congruent? If so, state the postulate or theorem you would use. Explain your reasoning.** **a.** Diagram a: A triangle \( \triangle EGH \) is displayed with right angles at \( \angle EGH \) and \( \angle EGF \). The sides FG and GH are marked on the triangle. **b.** Diagram b: A quadrilateral \( PQRS \) is displayed with diagonal PS intersecting it. Two angles on opposite sides of PS are marked. **Solution** **a.** The diagram shows that \( \angle EGH \) and \( \angle EGF \) are right angles. So, \( \angle EGH \cong \angle EGF \). Also, \( \overline{EG} \cong \overline{EG} \) by the Reflexive Property of Congruence. This is sufficient information to prove that the triangles are congruent by the Hypotenuse-Leg (HL) Theorem. **b.** In addition to the angles that are marked, \( \overline{PS} \cong \overline{PS} \) by the Reflexive Property of Congruence. Two pairs of corresponding angles and the one pair of corresponding sides are congruent. You can use the Angle-Side-Angle (ASA) Postulate to prove that \( \triangle PQS \cong \triangle RQS \).
Transcribed Image Text:**Example 1: Developing Proof** **Is it possible to prove that the triangles are congruent? If so, state the postulate or theorem you would use. Explain your reasoning.** **a.** Diagram a: A triangle \( \triangle EGH \) is displayed with right angles at \( \angle EGH \) and \( \angle EGF \). The sides FG and GH are marked on the triangle. **b.** Diagram b: A quadrilateral \( PQRS \) is displayed with diagonal PS intersecting it. Two angles on opposite sides of PS are marked. **Solution** **a.** The diagram shows that \( \angle EGH \) and \( \angle EGF \) are right angles. So, \( \angle EGH \cong \angle EGF \). Also, \( \overline{EG} \cong \overline{EG} \) by the Reflexive Property of Congruence. This is sufficient information to prove that the triangles are congruent by the Hypotenuse-Leg (HL) Theorem. **b.** In addition to the angles that are marked, \( \overline{PS} \cong \overline{PS} \) by the Reflexive Property of Congruence. Two pairs of corresponding angles and the one pair of corresponding sides are congruent. You can use the Angle-Side-Angle (ASA) Postulate to prove that \( \triangle PQS \cong \triangle RQS \).
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