First prove that triangles are congruent, then use CPCTC. H K Given: Prove: LFHG = LGFH O LGFH = LJHK 41 42 O LG = LJ Given that 21 and 22 are right
First prove that triangles are congruent, then use CPCTC. H K Given: Prove: LFHG = LGFH O LGFH = LJHK 41 42 O LG = LJ Given that 21 and 22 are right
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Given:
- \( \angle 1 \) and \( \angle 2 \) are right angles.
- \( H \) is the midpoint of \( \overline{FK} \).
To Prove:
- \( \overline{FG} \cong \overline{HJ} \)
### Steps for Proof:
1. **Identifying Right Angles**:
Given that \( \angle 1 \) and \( \angle 2 \) are right angles, the following statement holds because all right angles are congruent:
- \( \angle 1 \cong \angle 2 \)
\(\bigcirc\) \( \angle GFH \cong \angle LJK \)
2. **Midpoint Theorem**:
Given that \( H \) is the midpoint of \( \overline{FK} \), the following statement holds because the midpoint forms two congruent segments:
- \( \overline{FH} \cong \overline{HK} \)
\(\bigcirc\) \( \overline{FH} \cong \overline{HK} \)
3. **Corresponding Angles**:
Given \( \overline{FG} \parallel \overline{HJ} \), the following statement holds because lines cut by a transversal have congruent corresponding angles:
- \( \angle GFH \cong \angle LJK \)
\(\bigcirc\) \( \angle GFH \cong \angle LJK \)
4. **Applying ASA (Angle-Side-Angle)**:
Therefore, by the reason ASA, the next-to-last statement of the proof is the following:
- \( \triangle GFH \cong \triangle LJK \)
\(\bigcirc\) \( \triangle GFH \cong \triangle LJK \)
5. **Using CPCTC (Corresponding Parts of Congruent Triangles are Congruent)**:
Finally, by the reason CPCTC, the last statement of the proof is the following:
- \( \overline{FG} \cong \overline{HJ} \)
\(\bigcirc\) \( \overline{FG} \cong \overline](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb35f0eab-2452-4d20-90d7-c62e398afc80%2F3a2480e1-8ce0-4914-8556-ee0afcbc4d34%2Fteyrw4q_processed.png&w=3840&q=75)
Transcribed Image Text:First, prove that triangles are congruent, then use CPCTC.
Given:
- \( \angle 1 \) and \( \angle 2 \) are right angles.
- \( H \) is the midpoint of \( \overline{FK} \).
To Prove:
- \( \overline{FG} \cong \overline{HJ} \)
### Steps for Proof:
1. **Identifying Right Angles**:
Given that \( \angle 1 \) and \( \angle 2 \) are right angles, the following statement holds because all right angles are congruent:
- \( \angle 1 \cong \angle 2 \)
\(\bigcirc\) \( \angle GFH \cong \angle LJK \)
2. **Midpoint Theorem**:
Given that \( H \) is the midpoint of \( \overline{FK} \), the following statement holds because the midpoint forms two congruent segments:
- \( \overline{FH} \cong \overline{HK} \)
\(\bigcirc\) \( \overline{FH} \cong \overline{HK} \)
3. **Corresponding Angles**:
Given \( \overline{FG} \parallel \overline{HJ} \), the following statement holds because lines cut by a transversal have congruent corresponding angles:
- \( \angle GFH \cong \angle LJK \)
\(\bigcirc\) \( \angle GFH \cong \angle LJK \)
4. **Applying ASA (Angle-Side-Angle)**:
Therefore, by the reason ASA, the next-to-last statement of the proof is the following:
- \( \triangle GFH \cong \triangle LJK \)
\(\bigcirc\) \( \triangle GFH \cong \triangle LJK \)
5. **Using CPCTC (Corresponding Parts of Congruent Triangles are Congruent)**:
Finally, by the reason CPCTC, the last statement of the proof is the following:
- \( \overline{FG} \cong \overline{HJ} \)
\(\bigcirc\) \( \overline{FG} \cong \overline
Expert Solution
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We have to find out FG≌HJ
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