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How do you find the circumcenter of different types of triangle using cutting and folding method?
Suppose you have a triangle whose vertices are A, B and C, and the sides opposite these vertices are a, b and c, respectively. Cut out the triangle. Fold it so that vertex B meets vertex C. Mark the point where this fold is on side a. Mark this point as D and fold along AD. Fold it so that vertex A meets vertex C. Mark the point where this fold is on side b. Mark this point as E and fold along BE. Fold it so that vertex A meets vertex B. Mark the point where this fold is on side c. Mark this point as F and fold along CF. The three folds, AD, BE and CF meet at the circumcentre. You do not need all three - any two of them will do.
What is the bottom triangle at the 0 mark on the horizontal ruler?
Hanging indent is the term for the bottom triangle at the 0 mark on a horizontal ruler.
Why do all angles in a triangle add up to 180?
Draw two parallel lines (with points marked D and E on one, and F and G on the other). Mark point A on one line between D and E, and mark two points B and C on the other line between F and G. Join ABC to for a triangle: D_____________A_________________E ← point labels ------->---------+---------------------- ← first of the parallel lines _______________/\__________________ ______________/__\_________________ _____________/____\________________ ____________/______\_______________ ------->----+---------+---------------- ← second of the parallel lines F________B__________C__________G ← point labels (The underscores are there to keep the diagram in place - think of them like lines on the page of an exercise book.) Angles BAD + BAC + CAE add up to 180° as they are three angles on a straight line. Now angle ABC is the same as angle BAD as they are alternate (Z) angles Similarly, angle ACB is the same as angle CAE as they are alternate (Z) angles So substituting for equal angles, this gives: BAD + BAC + CAE = 180° → ABC + BAC + ACB = 180° But these three angles are the angles of the triangle ABC; thus the sum of the angles in a triangle is 180°.
How do you draw square root of 2 on a number line?
At the point 1, draw a perpendicular to the number line. Mark of a length of 1 unit on this line: call that point A.From the 0 on the number line, using a pair of compasses, measure the arc OA and use that length to mark the number line at sqrt(2).Rationale:You have a right angled triangle, with its right angle at the point 1. The base is 1 unit and the vertical height is 1 unit. So, by Pythagoras, the line from 0 to A is sqrt(2) units.At the point 1, draw a perpendicular to the number line. Mark of a length of 1 unit on this line: call that point A.From the 0 on the number line, using a pair of compasses, measure the arc OA and use that length to mark the number line at sqrt(2).Rationale:You have a right angled triangle, with its right angle at the point 1. The base is 1 unit and the vertical height is 1 unit. So, by Pythagoras, the line from 0 to A is sqrt(2) units.At the point 1, draw a perpendicular to the number line. Mark of a length of 1 unit on this line: call that point A.From the 0 on the number line, using a pair of compasses, measure the arc OA and use that length to mark the number line at sqrt(2).Rationale:You have a right angled triangle, with its right angle at the point 1. The base is 1 unit and the vertical height is 1 unit. So, by Pythagoras, the line from 0 to A is sqrt(2) units.At the point 1, draw a perpendicular to the number line. Mark of a length of 1 unit on this line: call that point A.From the 0 on the number line, using a pair of compasses, measure the arc OA and use that length to mark the number line at sqrt(2).Rationale:You have a right angled triangle, with its right angle at the point 1. The base is 1 unit and the vertical height is 1 unit. So, by Pythagoras, the line from 0 to A is sqrt(2) units.
How can you tell if three numbers equal a right triangle?
A right triangle is a triangle that has one 90 degree angle, and 2 other angles. Some special ones are 45-45-90, and 30-60-90. The sum of the angles in a triangle will always = 180 degrees. Since we know a triangle has 3 angles, and in particular, a right triangle has a 90 degree angle. We can say 180 degrees - 90 degrees = the other 2 angles. Add the other 2 angles in your triangle. Usually one is given as 90 degrees, or has a small square mark in the corner of the triangle to indicate that it is a right triangle. Once you add the other 2 angles, see if they add up to 90 degrees. If they do, you have a right triangle. If they do not, you either do not have a right triangle OR your triangle is broken and all 3 angles do not add up to 180 degrees.
