ABC is an equilateral triangle whose vertex A has the co-ordinates (0, √3). Find the co- ordinates of B and C.
1 answer:
Answer:
B = (-1, 0)
C = (1, 0)
Step-by-step explanation:
<u>Properties of an Equilateral Triangle</u>
- Three sides of <u>equal length</u>
- All interior angles are 60°
<u>Given</u>:
- ΔABC is an equilateral triangle
- Vertex A is at (0, √3)
Drawing an altitude from vertex A divides the triangle into two 30-60-90 triangles.
A 30-60-90 triangle is <u>special right-angled triangle</u> where:
- Angles are in the ratio 1 : 2 : 3
- Sides are in the ratio 1 : √3 : 2
Therefore, the formula for the sides is: b : b√3 : 2b, where:
- b = shortest side opposite the 30° angle
- b√3 = side opposite the 60° angle
- 2b = longest side (hypotenuse) is opposite the right angle
As Vertex A has the co-ordinates (0, √3), the <u>side opposite the 60° angle</u> is √3 units.
Using the ratios to find b (shortest side length):
b√3 = √3 ⇒ b = 1
As the altitude divides BC into two equal line segments, and the length of the shortest side of the right triangles is 1 unit, the coordinates of B are C are:
- B = (-1, 0)
- C = (1, 0)
Learn more about the 30-60-90 triangle here:
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Answer:
because they are opposite sides of a parallelogram.
Step-by-step explanation:
First of all, let us have a look at the definition of a parallelogram.
<em>A parallelogram is a closed 4 sided figure (i.e. a quadrilateral) made up with two pairs of straight lines such that the two pairs are parallel and equal to each other.</em>
<em></em>
For example, let us consider a quadrilateral ABCD as attached in the diagram in answer area.
The two pair of lines are:
AB, DC and BC, AD
For ABCD to be a parallelogram, the lines
AB and DC must be parallel to each other and AB = DC
AND
BC and AD must be parallel to each other and BC = DA
------------------------------
In the given question, we are given that the quadrilateral MNOP is a parallelogram.
The two pairs opposite lines are OP, NM and PM, ON.
As per the definition of a parallelogram,
OP and NM must be <em>parallel and equal </em>to each other.
AND
PM and ON must be <em>parallel and equal </em>to each other.
.
Hence proved.
Answer:
85°
Step-by-step explanation:
Please follow along with these directions on the attached picture so that this makes sense. I have labeled the picture with the variables I used and the angles I figured out.
Let's start in the top left corner. Remember: triangles always have 180°, and straight lines always have 180°.
180-115 = 65
65+85+x = 180, so x = 30
30+90+y = 180, so y = 60
180-155 = 25
25+60+z = 180, so z = 95
180-95 = 85°
