1. Geometric Twins

8 topics1 h

Chapter 1 of NCERT Mathematics for Class 7: Geometric Twins. Three sections — What congruence means, Congruence criteria for triangles and What congruence lets you prove. Eight videos, 1 h in all.

Worked answers to the 18 exercise questions in this chapter →

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Part 1

What congruence means

10 minSame shape and same size: superimposition as the testA sign painter must reproduce a symbol on a board standing somewhere else. He cannot carry the first board, and he cannot carry a memory.10 min · 12 partsहिंदी

Part 2

Congruence criteria for triangles

10 minSSS: three sidelengths fix a triangle completelyA triangular frame stands on the grass, wider than any ruler in the school. Three lengths are enough to rebuild it exactly.10 min · 12 partsहिंदी

9 minNaming congruent figures so the correspondence is unambiguousThe congruence sign is not the equals sign. Equals does not care which number you write first; this one relates two ordered lists.9 min · 12 partsहिंदी

9 minSAS, and why the angle has to be the included oneThe word included carries the whole of the SAS condition. Run the same construction twice, moving only the angle, and watch it break.9 min · 12 partsहिंदी

10 minASA and AAS: two angles are enough to fix the thirdAAS looks like a fifth thing to memorise. Because the three angles are locked to 180°, knowing two hands you the third for free.10 min · 12 partsहिंदी

9 minRHS: the right-angled special caseRHS is not an exception bolted onto the SSA warning. It is the case where the SSA ambiguity turns harmless.9 min · 12 partsहिंदी

Part 3

What congruence lets you prove

8 minAngles opposite equal sides are equalCongruence has been a test: two triangles arrive and you decide. This is where it turns into a tool you can use on one triangle.8 min · 12 partsहिंदी

9 minWhy every equilateral triangle has three 60° anglesEquilateral is a claim about lengths — three sides the same, nothing at all about angles. And yet the angles are forced.9 min · 12 partsहिंदी

What you will be able to do

State what has to be true of two figures for them to be congruent
State the SSS condition in the form the chapter states it
Read a congruence statement and say which vertex is claimed to match which
State the SAS condition and identify the included angle in a given triangle
State the ASA condition and identify the included side for a stated pair of angles
State the RHS condition, naming which three parts have to match
State the isosceles result: equal sides force the angles facing them to be equal
State what equilateral asserts, and what it does not directly assert

What this chapter assumes you already know

Measuring a length in centimetres with a ruler, and an angle in degrees with a protractor
Naming the corners of a figure with capital letters, and reading ∠ABC as the angle at B
Drawing a circle of a stated radius about a stated centre
The idea, from Class 6, that turning or flipping a shape does not change the shape
Drawing a circle of a given radius about a given point with a compass
Reading a length off a ruler and a measuring tape
A triangle has three sides and three angles, and knowing some of them may or may not pin down the rest
The idea of a fold line: a crease about which two halves land on each other

It builds directly on The four angles at a crossing: vertically opposite and linear pairs and Why the three angles of any triangle add to 180°.

Where people usually slip up

Sentences students actually say, taken from the notes the videos were made from. Each one is answered on the page of the video it belongs to.

"Congruent means the same shape."
"If it has been turned round, it is a different figure."
"Two figures that look alike are congruent."
"More measurements are always safer."
"A figure with three arms must have them evenly spread."
"Congruent and equal are the same word."
"Two circles crossing twice means the triangle is not determined."
"You need the angles as well, to be safe."