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Resources tagged with: Angles - points, lines and parallel lines

There are 70 NRICH Mathematical resources connected to Angles - points, lines and parallel lines , you may find related items under Angles, polygons, and geometrical proof .

Angles Inside

Draw some angles inside a rectangle. What do you notice? Can you prove it?

Robotic Rotations

How did the the rotation robot make these patterns?

Polygon Pictures

Can you work out how these polygon pictures were drawn, and use that to figure out their angles?

Triangle in a Trapezium

Can you find and prove the relationship between the area of a trapezium and the area of a triangle constructed within it?

Isosceles Seven

Is it possible to find the angles in this rather special isosceles triangle?

Polygon Rings

Join pentagons together edge to edge. Will they form a ring?

Same Length

Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?

Olympic Turns

This task looks at the different turns involved in different Olympic sports as a way of exploring the mathematics of turns and angles.

National Flags

This problem explores the shapes and symmetries in some national flags.

Which Solids Can We Make?

Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?

What Shape?

This task develops spatial reasoning skills. By framing and asking questions a member of the team has to find out what mathematical object they have chosen.

The Numbers Give the Design

Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.

Making Sixty

Why does this fold create an angle of sixty degrees?

Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?

Six Places to Visit

Can you describe the journey to each of the six places on these maps? How would you turn at each junction?

How Safe Are You?

How much do you have to turn these dials by in order to unlock the safes?

Round and Round and Round

Where will the point stop after it has turned through 30 000 degrees? I took out my calculator and typed 30 000 ÷ 360. How did this help?

Semi-regular Tessellations

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

Right Angles

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?

Subtended Angles

What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?

Triangles in Circles

Can you find triangles on a 9-point circle? Can you work out their angles?

Octa-flower

Join some regular octahedra, face touching face and one vertex of each meeting at a point. How many octahedra can you fit around this point?

Estimating Angles

How good are you at estimating angles?

Watch the Clock

During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

Angle Trisection

It is impossible to trisect an angle using only ruler and compasses but it can be done using a carpenter's square.

Quad in Quad

Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?

Flexi Quads

A quadrilateral changes shape with the edge lengths constant. Show the scalar product of the diagonals is constant. If the diagonals are perpendicular in one position are they always perpendicular?

Virtual Geoboard

A virtual geoboard that allows you to create shapes by stretching rubber bands between pegs on the board. Allows a variable number of pegs and variable grid geometry and includes a point labeller.

Pegboard Quads

Make different quadrilaterals on a nine-point pegboard, and work out their angles. What do you notice?

Angle Measurement: an Opportunity for Equity

Suggestions for worthwhile mathematical activity on the subject of angle measurement for all pupils.

Watch Those Wheels

Have you ever noticed the patterns in car wheel trims? These questions will make you look at car wheels in a different way!

Sweeping Hands

Use your knowledge of angles to work out how many degrees the hour and minute hands of a clock travel through in different amounts of time.

Right Angle Challenge

How many right angles can you make using two sticks?

Pythagoras of Samos was a Greek philosopher who lived from about 580 BC to about 500 BC. Find out about the important developments he made in mathematics, astronomy, and the theory of music.

Coordinates and Descartes

Have you ever wondered how maps are made? Or perhaps who first thought of the idea of designing maps? We're here to answer these questions for you.

Maurits Cornelius Escher

Have you ever noticed how mathematical ideas are often used in patterns that we see all around us? This article describes the life of Escher who was a passionate believer that maths and art can be intertwined.

Six circles around a central circle make a flower. Watch the flower as you change the radii in this circle packing. Prove that with the given ratios of the radii the petals touch and fit perfectly.

Lunar Angles

What is the sum of the angles of a triangle whose sides are circular arcs on a flat surface? What if the triangle is on the surface of a sphere?

LOGO Challenge 7 - More Stars and Squares

Can you use LOGO to create a systematic reproduction of a basic design? An introduction to variables in a familiar setting.

LOGO Challenge 8 - Rhombi

Explore patterns based on a rhombus. How can you enlarge the pattern - or explode it?

LOGO Challenge 1 - Star Square

Can you use LOGO to create this star pattern made from squares. Only basic LOGO knowledge needed.

Take the Right Angle

How many times in twelve hours do the hands of a clock form a right angle? Use the interactivity to check your answers.

Parallel Universe

An equilateral triangle is constructed on BC. A line QD is drawn, where Q is the midpoint of AC. Prove that AB // QD.

Similarly So

ABCD is a square. P is the midpoint of AB and is joined to C. A line from D perpendicular to PC meets the line at the point Q. Prove AQ = AD.

My train left London between 6 a.m. and 7 a.m. and arrived in Paris between 9 a.m. and 10 a.m. At the start and end of the journey the hands on my watch were in exactly the same positions but the minute hand and hour hand had swopped places. What time did the train leave London and how long did the journey take?

On a clock the three hands - the second, minute and hour hands - are on the same axis. How often in a 24 hour day will the second hand be parallel to either of the two other hands?

The points P, Q, R and S are the midpoints of the edges of a non-convex quadrilateral.What do you notice about the quadrilateral PQRS and its area?

A Problem of Time

Consider a watch face which has identical hands and identical marks for the hours. It is opposite to a mirror. When is the time as read direct and in the mirror exactly the same between 6 and 7?

Square World

P is a point inside a square ABCD such that PA= 1, PB = 2 and PC = 3. How big is angle APB ?

Clock Hands

This investigation explores using different shapes as the hands of the clock. What things occur as the the hands move.

Missing Angles

Related worksheets.

Find the missing angles in a triangle, around a point, in a quadrilateral, find opposite and supplementary angles, or find angles which require multi-step problem solving skills.

For more shape and space resources click here.

Game Objectives

New Maths Curriculum:

Year 3: Identify right angles, recognise that two right angles make a half-turn, three make three quarters of a turn and four a complete turn; identify whether angles are greater than or less than a right angle

Year 4: Identify acute and obtuse angles and compare and order angles up to two right angles by size

Year 5: Identify: multiples of 90°, angles at a point on a straight line and ½ a turn (total 180°); angles at a point and one whole turn (total 360°); reflex angles; and compare different angles

Year 6: Find unknown angles where they meet at a point, are on a straight line, and are vertically opposite

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Maths Games and Learning Activties for Fun

Category: angles – problem solving, angle chase – transum.

Angle Chase Use knowledge and reasoning to fill in the angles on the geometrical diagrams drawn inside rectangles. Level 1 – 31 angles to be found in a diagram with one set of parallel lines Level 2 – 42 angles Read More …

Kung Fu Angles – BBC

A quest that is solved using angles. Nice backdrops.

Gorilla – Count On

Two player game – gorillas throw bananas at each other across skyscrapers. Adjust force and angle to hit.

Bunny and Angles

A game to test estimation of angle size  – using 360 degrees – High level of accuracy required  

Gorilla – Mark Hanley

Two player game – gorillas throw bananas at each other across skyscrapers. Adjust force and angle to hit.  

Sailing Challenge – eChalk

Measure and estimate the angles of the boat’s courses.  

A quest that is solved using angles. Nice backdrops.  

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Angle Worksheets: Add Insight to Your Preparation

This far-from-exhaustive list of angle worksheets is pivotal in math curriculum. Whether it is basic concepts like naming angles, identifying the parts of an angle, classifying angles, measuring angles using a protractor, or be it advanced like complementary and supplementary angles, angles formed between intersecting lines, or angles formed in 2D shapes we have them all covered for students in grade 4 through high school. Application seals concepts in the minds of children, and hence adding a little challenge into the routine in the form of free worksheets is definitely not a bad idea.

List of Angle Worksheets

Parts of an Angle

Naming Angles

Acute, Right, and Obtuse Angles

Classifying Angles

Reading Protractors

Measuring Angles

Drawing Angles

Estimating Angles

Angles on a Straight Line

Angles Around a Point

• Complementary & Supplementary Angles

Adjacent Angles

Vertical Angles

Linear Pairs of Angles

Pairs of Angles

Angles Formed by a Transversal

Angles in Shapes

Explore the angle worksheets in detail.

How about some practice in identifying the vertex and arms of an angle? Get ahead of the pack with these parts of an angle pdfs and practice identifying and naming the vertex and arms of an angle.

Are you aware of the four ways of naming angles? Buckle up with these printable worksheets, and watch how accurately and effortlessly children name angles using the three points.

Spark interest and encourage children to identify acute, right, and obtuse angles with a bunch of fun-filled exercises like recognizing angles in a clock, angle types in real-life objects, and a lot more!

Become twice as conversant with identifying, classifying, and drawing all six types of angles: acute, right, obtuse, straight, reflex, and complete angles with this collection of pdfs.

Use the protractor tool like a pro to measure and draw angles. Printable protractor templates, a chart illustrating the parts and use of the tool, and protractor reading exercises await students in elementary school.

Reading the correct scale of the protractor to measure angles: the inner or outer scale, measuring and classifying angles, and solving linear equations are the skills grade 4 and grade 5 students acquire with these exercises.

Show your students how to construct angles using a protractor with these drawing angle pdfs. The exercises include constructing angles with 1° increments or 5°, drawing reflex angles, and more.

Expert-level skills aren’t built in a day, to acquire superior skills in estimating angles 4th grade and 5th grade children need to bolster practice with our printable estimating angles worksheets.

Work your way through this compilation of worksheets and examine the angles on a straight line that add up to 180°. Grade 4 and grade 5 students find the measures of the unknown angles by subtracting the given angles from 180°.

Did you know that the angles around a point add up to 360°? Keep this fact in mind as you figure out the measures of the unknown angles by adding the given angles and subtracting the sum from 360°.

Complementary and Supplementary Angles

If it's a pair of angles you see and are trying to figure out if they make a complementary or supplementary pair, the trick is just adding them up and if their sum is 90° they are complementary and if it is 180° they are supplementary. These worksheets are a sure-shot hit with 6th grade and 7th grade learners.

Explore this bunch of printable adjacent angles worksheets to get a vivid picture of the angle addition property exhibited by angles that share the same vertex and are next to each other.

Linked here are exercises on angles formed by intersecting lines! Know the congruent properties of vertical angles or vertically opposite angles and apply them to determine unknown angle measures.

Two angles that are both adjacent and supplementary are a linear pair. The measure of such a pair sum up to 180°. Get to the heart of such angle pairs with these pdf worksheets and solve equations for the unknown angle measures.

Tap your grade 7, and grade 8 student’s potential in identifying the different pairs of angles such as complementary and supplementary angles, linear pair, vertical angles and much more with our engaging set of worksheets.

Construct additional and experiential knowledge with these 8th grade and high school handouts to comprehend the seven types of angle pairs formed by a transversal that include corresponding angles, alternate angles, and consecutive angles.

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Reasoning with Angles

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

22 February 2018

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Unit 10 - 3 weeks

The PowerPoint file contains slides you can use in the classroom to support each of the learning outcomes for this unit, listed below. Geometry topics are not covered by the NCETM Primary Mastery Professional Development materials. Therefore, some slides for this unit have been additionally created to provide the high-level overview to address each learning outcome. However, they do not provide the level of detail seen in other units, so teachers will need to supplement slides with other high quality materials available to them. You should also refer to the national curriculum to ensure coverage. There are also links to the ready-to-progress criteria detailed in the DfE Primary Mathematics Guidance 2020 .

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