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Given: Line l is the perpendicular bisector of BC; A is on l. Prove: AB = AC B Theorem 4-6 If a point is equidistant from the endpoints of a segment, then the point lies on the perpendicular bisector of the segment. Given: AB = AC Prove: A is on the perpendicular bisector of BC. Plan for Proof: The perpendicular bisector of BC must 112 B C contain the midpoint of BC and be perpendicular to BC. Draw an auxiliary line containing A that has one of these properties and prove that it has the other property as well. For example, first draw a segment from A to the midpoint X of BC. You can show that AX 1 BC if you can show that Z1=2. Since these angles are corresponding parts of two triangles, first show that AAXB = AAXC. In the proof of Theorem 4-6 other auxiliary

Given: Line l is the perpendicular bisector of BC; A is on l. Prove: AB = AC B Theorem 4-6 If a point is equidistant from the endpoints of a segment, then the point lies on the perpendicular bisector of the segment. Given: AB = AC Prove: A is on the perpendicular bisector of BC. Plan for Proof: The perpendicular bisector of BC must 112 B C contain the midpoint of BC and be perpendicular to BC. Draw an auxiliary line containing A that has one of these properties and prove that it has the other property as well. For example, first draw a segment from A to the midpoint X of BC. You can show that AX 1 BC if you can show that Z1=2. Since these angles are corresponding parts of two triangles, first show that AAXB = AAXC. In the proof of Theorem 4-6 other auxiliary

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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Given: Line l is the perpendicular bisector of BC; A is on l. Prove: AB = AC B Theorem 4-6 If a point is equidistant from the endpoints of a segment, then the point lies on the perpendicular bisector of the segment. Given: AB = AC Prove: A is on the perpendicular bisector of BC. Plan for Proof: The perpendicular bisector of BC must 112 B C contain the midpoint of BC and be perpendicular to BC. Draw an auxiliary line containing A that has one of these properties and prove that it has the other property as well. For example, first draw a segment from A to the midpoint X of BC. You can show that AX I BC if you can show that 21=2. Since these angles are corresponding parts of two triangles, first show that AAXB = AAXC. In the proof of Theorem 4-6 other auxiliary
Transcribed Image Text:Given: Line l is the perpendicular bisector of BC; A is on l. Prove: AB = AC B Theorem 4-6 If a point is equidistant from the endpoints of a segment, then the point lies on the perpendicular bisector of the segment. Given: AB = AC Prove: A is on the perpendicular bisector of BC. Plan for Proof: The perpendicular bisector of BC must 112 B C contain the midpoint of BC and be perpendicular to BC. Draw an auxiliary line containing A that has one of these properties and prove that it has the other property as well. For example, first draw a segment from A to the midpoint X of BC. You can show that AX I BC if you can show that 21=2. Since these angles are corresponding parts of two triangles, first show that AAXB = AAXC. In the proof of Theorem 4-6 other auxiliary
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