Currently viewing the tag: "Angles"
If you know the sizes of the angles marked with coloured dots in the diagram which angles can you find by calculation? Explain your reasoning.
If you also know that AB and CD are parallel which angles can you find?
What extra information do you need to find all the numbered angles?
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In the diagram the line OS is perpendicular to the lines OR and PQ.
The line RS is a tangent at P to the circle centre O and radius 1 unit.
Find the lengths OQ, PQ, PS, OS, OR and RP.
If OS and OR lie on the coordinate axes, what are the coordinates […]
The point E is inside the square ABCD and AEB is an equilateral triangle. Find the angles EBC, BEC and ECD and give reasons for your answers.
Click for Teacher-Notes-GEO-PROB.
We say that a shape tessellates if we can fit together copies of it to cover a flat surface without leaving any gaps and this covering can be extended in all directions.
The question here is “What can we find out about tessellating different quadrilaterals?”
It’s quite easy to see how […]
Draw chords to cut a regular hexagon
(a) into two pieces which, when put together, make a parallelogram;
(b) into three pieces which, when put together, make a rhombus;
(c) into four pieces which, when put together, make two equilateral triangles.
(d) What angles can you find in each of your shapes?
(e) If […]
This is a unit circle with a tangent at A.
The angle marked in the diagram is angle a.
Copy the diagram and find all the angles in terms of the angle a.
Find the six line segments in the diagram corresponding to sina, cosa, tana, 1/sina, 1/cosa and 1/tana.
Find the areas of […]
The hour and minute hands of my clock are at right angles.
How many degrees does each hand move forward in one minute? How long will it be before they are at right angles again?
Be careful, it will not be at half past three!
See the AIMSSEC Notes for Teachers.
This problem […]
Investigate different triangles PQR where the angle QPR is 40 degrees. Choose your own angles at Q and R, for example someone might choose 90 degrees and 50 degrees and someone else 62 degrees and 78 degrees.
Accurately draw the internal bisectors of the angles at Q and R to meet […]
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