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How do you find the third vertex of a triangle when given two other points and an area?
Wiki User
∙ 13y ago
You cannot. At least, not one point.
If the distance between the two given points is b, and the area of the triangle is A, then let h = 2A/b
Then draw two lines parallel to the line formed by the two given points - one above and one below, each of these lines being at a distance h from the first line.
Any point on either of these two lines will meet your requirements.
Wiki User
∙ 13y ago
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Which is the opposite and adjacent sides in a triangle?
Each triangle has three sides and three vertices. The opposite side of a triangle is the side that is not adjacent to the specified vertex. The other two sides are adjacent sides to the specified vertex. Circular definition? Yes - Here is the formal definition... Given a triangle with vertices A, B, and C, the side AB is adjacent to the angles ABC and BAC, and it is opposite to the angle ACB.
When you use a formula to calculate the area of a triangle does it matter which base - height pair you use.?
The side you use as the base does not matter. What does matter is that the height is the perpendicular distance between this side and the other vertex. If there is a right angle in the triangle, then use the two sides next to it as the base and height. Otherwise a bit of trigonometry will be required to work out the height of the triangle if it is not given.
Why is the sum of a triangle's angles will always equal 180 degrees?
By historical convention a complete circle is 360 degrees, so if you take a point on a straight line and rotate until you face the other way the total angle is 180 degrees. Now if you take any two parallel lines, any distance apart, and mark a point anywhere on one line, and two points anywhere on the other line, then by varying these two lines and three points you can form any shaped triangle by joining up the three points. Now because the lines are parallel there is no angle between them, so a straight line drawn from one to the other will provide two identical angles rotated 180 degrees about. Call these two identical angles A. Now if you take a new line from one of the intersections to a new point on the other parallel line the same applies and we will call the two new identical angles B. If you draw this out you will have a triangle with a base with angles A & B and for the sake of convention we will call the remaining angle at the peak of the triangle C. The total angle at the peak of the triangle enabling one of the parallel lines to rotate and face the other way is, as we have said, 180 degrees but is also equal to C plus the rotated angles A and B. therefore A+B+C = 180 Degrees which is the same as your three angles in the triangle. ( It's much easier with diagrams). Or, you can work simpler like this: In a piece of paper draw a conveniently large scalene triangle ABC. Write 1 under the vertex A, 2 under the vertex B, and 3 under the vertex C (these numbers represent respectively the measure of angles A, B, and C). Cut the paper, and on another piece of paper point the three vertices A, B, and C. Connect these three points, and write the corresponding numbers 1, 2, and 3 respectively at vertices A, B, and C. Take the triangle and put the vertex C at the point A, A at C, and point B. Connect point B with others, and write the corresponding numbers under the corresponding vertices. Take the triangle and put the vertex C at the point B, the vertex B at A, and point A. Connect point A with others, and write the corresponding numbers under the corresponding vertices again. You can see that a straight angle is formed, whose measure is equal to the sum of the angles 1 + 3 + 2. Since the measure of a straight angle is equal to 180 degrees, then we say that the sum of the angles of a triangle is eaqual to 180 degrees (m A = 1) + (m B = 2) + (m C = 3) = 180 degrees.
How do you reflect a shape with a given line?
Pick a vertex of the original shape.Draw a perpendicular to the given line.Double the length of this perpendicular. The end point is the image of the original vertex.Repeat for all other vertices of the original shape.Join the vertices of the image.
What is the maximum number of points at which the sides of a triangle can intersect the sides of another triangle?
The wording of the question leaves room for two interpretations, but I believe the expected answer is six. Think of the "Star of David" (also known as the Magen David). See the "Web Link" at the bottom left. But that's for only one orientation. There are an infinite number of points on each line segment, so if you rotate one triangle with respect to the other, different pairs of points will be involved.
What do you call the point of the triangle?
The point of a triangle is called a vertex, same goes with rectangles and all other shapes with points.
How do you construct an isosceles triangle when base and angle at the vertex is given?
First find 180 minus the vertex angle and divide that by 2 to get the other angles. Then solve the other sides by using sin(vertex angle)/base=sin(other angles)/other sides.
A perpendicular segment with one endpoint at a vertex and the other endpoint on the side opposite that vertex?
Altitude: The altitude of a triangle is a perpendicular segment that connects a vertex and its opposite side. Let's construct the altitude of a triangle using a new triangle.
How would you construct an isosceles triangle if only given the vertex angle and the radius of the circumscribed circle?
You have an isosceles triangle, and a circle that is drawn around it. You know the vertex angle of the isosceles triangle, and you know the radius of the circle. If you use a compass and draw the circle according to its radius, you can begin your construction. First, draw a bisecting cord vertically down the middle. This bisects the circle, and it will also bisect your isosceles triangle. At the top of this cord will be the vertex of your isosceles triangle. Now is the time to work with the angle of the vertex. Take the given angle and divide it in two. Then take that resulting angle and, using your protractor, mark the angle from the point at the top of the cord you drew. Then draw in a line segment from the "vertex point" and extend it until it intersects the circle. This new cord represents one side of the isosceles triangle you wished to construct. Repeat the process on the other side of the vertical line you bisected the circle with. Lastly, draw in a line segment between the points where the two sides of your triangle intersect the circle, and that will be the base of your isosceles triangle.
What are vertices from a triangle?
The vertices of a triangle are the endpoints. In other words, when the sides of the triangle intersect, they form a vertex of a triangle. A triangle has a total of three vertices.
What points in a triangle is not necessarily collinear with the other points in the triangle?
The following is the answer.
When you use the distance formula you are calculating the length of a right triangle which goes between two given points?
Yes, the Euclidean distance is the length of the hypotenuse of the right angled triangle whose other two vertices are at the two given points.
What is the maximum vertex angle in an isosceles triangle?
an isosceles triangle can have any vertex angle less than 180 and greater than 0, as long the other two angles are equal. an isosceles triangle with a vertex of 179 degrees would just have the other two angles be 0.5 degrees. A right triangle with matching angles (both 45 degrees) would be both a right triangle and isosceles triangle.
Where is the vertex of a triangle?
"Vertex" is the plane-geometry term for a corner, so a triangle has three, a square (or any other four-sided shape) has four, a pentagon has five, and so on.
Are the diagonals of an isosceles triangle perpendicular?
There are no 'diagonals' in a triangle. Each vertex is connected to both of the other vertices, by the sides.
Which is the opposite and adjacent sides in a triangle?
Each triangle has three sides and three vertices. The opposite side of a triangle is the side that is not adjacent to the specified vertex. The other two sides are adjacent sides to the specified vertex. Circular definition? Yes - Here is the formal definition... Given a triangle with vertices A, B, and C, the side AB is adjacent to the angles ABC and BAC, and it is opposite to the angle ACB.
Does diagonals of right angled triangle bisect each other?
A diagonal is normally defined as a straight line joining a vertex of a polygon with any vertex other than an adjoining vertex (lines joining a vertex to an adjoining vertex would simply be a side of the polygon). Since a triangle has only got adjoining vertices, it has no diagonals. Since there are no diagonals, they cannot bisect one another.
