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10) Given: FL = FK;LA= KA Prove: LJ= KJ STATEMENTS REASONS

10) Given: FL = FK;LA= KA Prove: LJ= KJ STATEMENTS REASONS

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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do 10 please

### Geometric Proof Exercise #### Given: FL ≅ FK; LA ≅ KA #### Prove: LJ ≅ KJ #### Solution: **Diagram Description:** The diagram illustrates a kite-shaped quadrilateral FLAK with a diagonal LJ intersecting at a right angle with another diagonal FK. Points F, L, A, and K form the vertices of the quadrilateral, while point J is the intersection of the diagonals. **Proof Structure:** | **STATEMENTS** | **REASONS** | |----------------|-------------| | | | Feel free to fill in the "Statements" and "Reasons" columns as you progress through the proof. #### Explanation: 1. **FL ≅ FK:** This indicates that segment FL is congruent to segment FK. 2. **LA ≅ KA:** This indicates that segment LA is congruent to segment KA. From these givens, we aim to prove that the segments LJ and KJ are congruent by filling in the logical steps in the proof. To do this, use properties of kites and congruent triangles that arise within the figure. This exercise helps solidify understanding of geometric proofs, specifically those involving congruent segments within kites and related figures.
Transcribed Image Text:### Geometric Proof Exercise #### Given: FL ≅ FK; LA ≅ KA #### Prove: LJ ≅ KJ #### Solution: **Diagram Description:** The diagram illustrates a kite-shaped quadrilateral FLAK with a diagonal LJ intersecting at a right angle with another diagonal FK. Points F, L, A, and K form the vertices of the quadrilateral, while point J is the intersection of the diagonals. **Proof Structure:** | **STATEMENTS** | **REASONS** | |----------------|-------------| | | | Feel free to fill in the "Statements" and "Reasons" columns as you progress through the proof. #### Explanation: 1. **FL ≅ FK:** This indicates that segment FL is congruent to segment FK. 2. **LA ≅ KA:** This indicates that segment LA is congruent to segment KA. From these givens, we aim to prove that the segments LJ and KJ are congruent by filling in the logical steps in the proof. To do this, use properties of kites and congruent triangles that arise within the figure. This exercise helps solidify understanding of geometric proofs, specifically those involving congruent segments within kites and related figures.
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