in abc triangle d is a point on bc such that angle adc = 90 degrees then ad is called -------
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7th
Maths
Congruence of Triangles
Criteria for Triangle Congruence
In Δ ABC , D is a point on ...
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Asked on December 30, 2019 by
Rushi Kuruvila
In ΔABC, D is a point on BC such that AB = AD = BD = DC. then
∠ADC:∠C=4:1
State whether the above statement is true or false.
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ANSWER
Here, AB,BD,AD are sides of a triangle. These sides are given equal. Hence the triangle is an equilateral triangle.
Thus, ∠ADB=60
∘
In △ADC,
AD=CD
Thus, ∠ADC=∠ACD=y (Isosceles triangle property)
Now, ∠ADB=∠ADC+∠ACD
60=y+y
y=30
∘
∠ACD=30
∘
∠ADC+∠ADB=180 (Angles on a straight line)
60+∠ADC=180
∠ADC=120
∘
Hence,
∠C
∠ADC
=
30
120
∠C
∠ADC
=4:1
Step-by-step explanation:
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