1.Is it possible to draw an angle of 46 degree using ruler and compass? What is the measure of an angle which is closest to the given angle and can be draw using a ruler and compass?
Answers
Step-by-step explanation:
This construction works by creating an isosceles right triangle, which is a 45-45-90 triangle. The image below is the final drawing above with the red items added.
Argument Reason
1 Line segment AB is perpendicular to PQ. Constructed that way. See Constructing the perpendicular bisector of a line.
2 Triangle APC is a right triangle Angle ACP is 90° (from step 1)
3 Line segments CP,CA are congruent Drawn with same compass width
4 Triangle ∆APC is isosceles. CP = AC
5 Angle APC has a measure of 45°. In isosceles triangle APC, base angles CPA and CAP are congruent. (See Isosceles Triangles). The third angle ACP is 90° and the interior angles of a triangle always add to 180. So both base angles CPA and CAP are 45°.
- Q.E.D
Try it yourself
Click here for a printable worksheet containing two 45° angle exercises. When you get to the page, use the browser print command to print as many as you wish. The printed output is not copyright.
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Lines
Introduction to constructions
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Sum of n line segments
Difference of two line segments
Perpendicular bisector of a line segment
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Perpendicular from endpoint of a ray
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Parallel line through a point (angle copy)
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Complementary angle
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Equilateral triangle
30-60-90 triangle, given the hypotenuse
Triangle, given 3 sides (sss)
Triangle, given one side and adjacent angles (asa)
Triangle, given two angles and non-included side (aas)
Triangle, given two sides and included angle (sas)
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Triangle midsegment
Triangle altitude
Triangle altitude (outside case)
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Right Triangle, given both legs (LL)
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Right Triangle, given one leg and one angle (LA)
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Triangle incenter
Triangle circumcenter
Triangle orthocenter
Triangle centroid
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Tangent at a point on the circle
Tangents through an external point
Tangents to two circles (external)
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Incircle of a triangle
Focus points of a given ellipse
Circumcircle of a triangle
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Non-Euclidean constructions
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