In - ABC - AD is the perpendicular bisector of BC see the given figure- Show that - ABC is an isosceles triangle in which AB - AC-

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Standard IX

Mathematics

ASA Criteria for Congruency

In Δ ABC , AD...

Question

In ΔABC, AD is the perpendicular bisector of BC (see the given figure). Show that ΔABC is an isosceles triangle in which AB = AC.

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Solution

In ΔADC and ΔADB,

AD = AD (Common)

∠ADC =∠ADB (Each 90º)

CD = BD (AD is the perpendicular bisector of BC)

∴ ΔADC ≅ ΔADB (By SAS congruence rule)

∴AB = AC (By CPCT)

Therefore, ABC is an isosceles triangle in which AB = AC.

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In ΔABC, AD is the perpendicular bisector of BC (see the given figure). Show that ΔABC is an isosceles triangle in which AB = AC.

In ΔADC and ΔADB, AD = AD (Common) ∠ADC =∠ADB (Each 90º) CD = BD (AD is the perpendicular bisector of BC) ∴ ΔADC ≅ ΔADB (By SAS congruence rule) ∴AB = AC (By CPCT) Therefore, ABC is an isosceles triangle in which AB = AC.

In ΔADC and ΔADB,

AD = AD (Common)

∠ADC =∠ADB (Each 90º)

CD = BD (AD is the perpendicular bisector of BC)

∴ ΔADC ≅ ΔADB (By SAS congruence rule)

∴AB = AC (By CPCT)

Therefore, ABC is an isosceles triangle in which AB = AC.