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1 answer:
Answer:
BD = <u>1</u> unit
AD = <u>1</u> unit
AB = <u>1.6</u> units
AC = <u>1.6</u> units
Step-by-step explanation:
In the picture attached, the triangle ABC is shown.
Given that triangle ABC is isosceles, then ∠B = ∠C
∠A + ∠B + ∠C = 180°
36° + 2∠B = 180°
∠B = (180° - 36°)/2
∠B = ∠C = 72°
From Law of Sines:
sin(∠A)/BC = sin(∠B)/AC = sin(∠C)/AB
(Remember that BC is 1 unit long)
AB = AC = sin(72°)/sin(36°) = 1.6
In triangle ABD, ∠B = 72°/2 = 36°, then:
∠A + ∠B + ∠D = 180°
36° + 36° + ∠D = 180°
∠D = 180° - 36° - 36° = 108°
From Law of Sines:
sin(∠A)/BD = sin(∠B)/AD = sin(∠D)/AB
(now ∠A = ∠B)
BD = AD = sin(∠A)*AB/sin(∠D)
BD = AD = sin(36°)*1.6/sin(108°) = 1
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Answer:
Given information: WY=ZX, A is the midpoint of WY and A is the midpoint of ZX.
To prove : WA =ZA
Proof:
A is the midpoint of WY, it means A divides WY in two equal parts.
So, WY is twice of WA.
.... (1)
A is the midpoint of ZX, it means A divides ZX in two equal parts.
So, ZX is twice of ZA.
... (2)
(Given)
Substitute the values from equation (1) and (2).
Divide both sides by 2.
Hence proved.