6. Triangle ABC is an isosceles triangle in which AB = AC.
Side BA is produced to D such that AD = AB
(see Fig. 7.34). Show that angle BCD is a right angle.
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Answers
In △ABC, we have
AB=AC ∣
given
∠ACB=∠ABC ... (1) ∣ Since angles opp. to equal sides are equal
Now,
AB=AD ∣
Given
∴AD=AC ∣ Since AB=AC
Thus , in △ADC, we have
AD=AC
⇒∠ACD=∠ADC ... (2) ∣
Since angles opp. to equal sides are equal
Adding (1) and (2) , we get
∠ACB+∠ACD=∠ABC+∠ADC
⇒∠BCD=∠ABC+∠BDC ∣ Since∠ADC=∠BDC
⇒∠BCD+∠BCD=∠ABC+∠BDC+∠BCD ∣ Adding ∠BCD on both sides
⇒2∠BCD=180
∘
∣ Angle sum property
⇒∠BCD=90
∘
Hence, ∠BCD is a right angle.
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Answer:
The eye is made up of a number of parts, including the iris, pupil, cornea, and retina. The eye has six muscles which control the eye movement, all providing different tension and torque. The eye works a lot like a camera, the pupil provides the f-stop, the iris the aperture stop, the cornea resembles a lens.
Step-by-step explanation:
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