ABCD is a rhombus in which the altitude from D to side AB bisects AB.Find the angles of the rhombus
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Given - ABCD is a Rhombus , is the altitude on AB then AE = EB.
To Find - ∠A ,∠C , ∠B and ∠D
Proof - In a ΔAED and ΔBED,
DE = DE ( common line)
∠AED = ∠BED ( right angle)
AE = EB ( DE is an altitude)
∴ ΔAED ≅ ΔBED ( SAS property)
∴ AD = BD ( by C.P.C.T)
But AD = AB ( sides of rhombus are equal)
⇒ AD = AB = BD
∴ ABD is an equilateral traingle.
∴ ∠A = 60°
⇒ ∠A = ∠C = 60° (opposite angles of rhombus are equal)
But Sum of adjacent angles of a rhombus is supplimentary.
∠ABC + ∠BCD = 180°
⇒ ∠ABC + 60°= 180°
⇒ ∠ABC = 180° - 60° = 120°.
∴ ∠ABC = ∠ADC = 120°.(opposite angles of rhombus are equal)
∴ Angles of rhombus are ∠A = 60° and ∠C = 60° , ∠B = ∠D = 120°.
To Find - ∠A ,∠C , ∠B and ∠D
Proof - In a ΔAED and ΔBED,
DE = DE ( common line)
∠AED = ∠BED ( right angle)
AE = EB ( DE is an altitude)
∴ ΔAED ≅ ΔBED ( SAS property)
∴ AD = BD ( by C.P.C.T)
But AD = AB ( sides of rhombus are equal)
⇒ AD = AB = BD
∴ ABD is an equilateral traingle.
∴ ∠A = 60°
⇒ ∠A = ∠C = 60° (opposite angles of rhombus are equal)
But Sum of adjacent angles of a rhombus is supplimentary.
∠ABC + ∠BCD = 180°
⇒ ∠ABC + 60°= 180°
⇒ ∠ABC = 180° - 60° = 120°.
∴ ∠ABC = ∠ADC = 120°.(opposite angles of rhombus are equal)
∴ Angles of rhombus are ∠A = 60° and ∠C = 60° , ∠B = ∠D = 120°.
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Raghunath answered 3 year(s) ago
Find the all angles of a rhombus .
ABCD is a rhombus in which the altitude from D to side AB bisect AB. Find the angle of a rhombus .
Class-VIII Maths
person
Asked by Devendra
Dec 4
0 Like 2964 views
edit Answer Like Follow
1 Answers
Top Recommend | Recent
person
Raghunath , SubjectMatterExpert
Member since Apr 11 2014
Sol:
Given that ABCD is a rhombus.DE is the altitude on AB then AE = EB.
In a ΔAED and ΔBED,
DE = DE ( common line)
∠AED = ∠BED ( right angle)
AE = EB ( DE is an altitude)
∴ ΔAED ≅ ΔBED ( SAS property)
∴ AD = BD ( by C.P.C.T)
But AD = AB ( sides of rhombus are equal)
⇒ AD = AB = BD
∴ ABD is an equilateral traingle.
∴ ∠A = 60°
⇒ ∠A = ∠C = 60° (opposite angles of rhombus are equal)
But Sum of adjacent angles of a rhombus is supplimentary.
∠ABC + ∠BCD = 180°
⇒ ∠ABC + 60°= 180°
⇒ ∠ABC = 180° - 60° = 120°.
∴ ∠ABC = ∠ADC = 120°.(opposite angles of rhombus are equal)
∴ Angles of rhombus are ∠A = 60° and ∠C = 60° , ∠B = ∠D = 120°.
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Raghunath answered 3 year(s) ago
Find the all angles of a rhombus .
ABCD is a rhombus in which the altitude from D to side AB bisect AB. Find the angle of a rhombus .
Class-VIII Maths
person
Asked by Devendra
Dec 4
0 Like 2964 views
edit Answer Like Follow
1 Answers
Top Recommend | Recent
person
Raghunath , SubjectMatterExpert
Member since Apr 11 2014
Sol:
Given that ABCD is a rhombus.DE is the altitude on AB then AE = EB.
In a ΔAED and ΔBED,
DE = DE ( common line)
∠AED = ∠BED ( right angle)
AE = EB ( DE is an altitude)
∴ ΔAED ≅ ΔBED ( SAS property)
∴ AD = BD ( by C.P.C.T)
But AD = AB ( sides of rhombus are equal)
⇒ AD = AB = BD
∴ ABD is an equilateral traingle.
∴ ∠A = 60°
⇒ ∠A = ∠C = 60° (opposite angles of rhombus are equal)
But Sum of adjacent angles of a rhombus is supplimentary.
∠ABC + ∠BCD = 180°
⇒ ∠ABC + 60°= 180°
⇒ ∠ABC = 180° - 60° = 120°.
∴ ∠ABC = ∠ADC = 120°.(opposite angles of rhombus are equal)
∴ Angles of rhombus are ∠A = 60° and ∠C = 60° , ∠B = ∠D = 120°.
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