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ABC is an equilateral triangle. If m∠DAC = m∠DCA = 40°, cho

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ABC is an equilateral triangle. If m∠DAC = m∠DCA = 40°, cho [#permalink] New post   08 Jan 2021, 10:30
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\(\triangle{ABC}\) is an equilateral triangle. If \(m∠DAC = m∠DCA = 40°\), choose all the true statements.

A. AD = DC
B. AD < BC
C. m∠DAB = m∠DCB
D. m∠ADC > m∠DCB
E. CE = EA


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A,B,C,E
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Re: ABC is an equilateral triangle. If m∠DAC = m∠DCA = 40°, cho [#permalink] New post   18 Jan 2021, 19:19
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By geometrical properties of triangles, A,B,C are true;

For E, since, as non-vertex angles are equal, consecutive sides are equal, this figure is considered as a kite. Non-vertex side diagonal is bisected by diagonal from the vertex side.
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Re: ABC is an equilateral triangle. If m∠DAC = m∠DCA = 40°, cho [#permalink] New post   21 Jan 2021, 12:37
why option d is wrong?
after calculation measure of angle BCD =100 and angle ADC=120
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Re: ABC is an equilateral triangle. If m∠DAC = m∠DCA = 40°, cho [#permalink] New post   21 Jan 2021, 12:49
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void wrote:
why option d is wrong?
after calculation measure of angle BCD =100 and angle ADC=120


I think you'll find that ∠ADC=100° degrees (since ∠DCA = ∠CAD = 40°)
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Re: ABC is an equilateral triangle. If m∠DAC = m∠DCA = 40°, cho [#permalink] New post   21 Jan 2021, 20:58
you are right ...calcullation mistake on myside .
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Re: ABC is an equilateral triangle. If m∠DAC = m∠DCA = 40°, cho [#permalink] New post   28 Mar 2021, 01:40
can anyone tell me the geometrical property used for option B.

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Re: ABC is an equilateral triangle. If m∠DAC = m∠DCA = 40°, cho [#permalink] New post   28 Mar 2021, 05:10
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arjunbir wrote:
can anyone tell me the geometrical property used for option B.

Thanks
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arjunbir

Greater the interior angle, greater is the side opposite to it

In triangle ADC, AD is opposite to 40 degree whereas AC is opposite to 100 degrees.
Also, AC = AB = BC

So, AD < BC
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Re: ABC is an equilateral triangle. If m∠DAC = m∠DCA = 40°, cho [#permalink] New post   28 Mar 2021, 08:48
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KarunMendiratta wrote:
arjunbir wrote:
can anyone tell me the geometrical property used for option B.

Thanks
Kind Regards


arjunbir

Greater the interior angle, greater is the side opposite to it

In triangle ADC, AD is opposite to 40 degree whereas AC is opposite to 100 degrees.
Also, AC = AB = BC

So, AD < BC



Thank you Sir
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Re: ABC is an equilateral triangle. If mDAC = mDCA = 40°, cho [#permalink] New post   15 May 2022, 05:21
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