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2 years ago

Which pairs of figures are congruent? Which pairs are similar?

Mathematics

1 answer:

dybincka [34]2 years ago

5 0

Answer: Look at the explanation

Step-by-step explanation: To understand what figures are congruent and what figures are similar, you need to understand what the terms mean.

Congruent figures have the same shape and size.

Similar figures have the same shape but different size.

The 1st figure is not congruent but it is similar.

2nd figure is congruent and similar which are rectangles. Wheather the figure is rotated or reflected, it is still congruent and similar.

3rd figure is both, congruent and similar which are both triangles.

4th figure is neither. There is a circle and an elipse, which are both round but different shapes.

By knowing the terms congruent and similar, you should have no problem in identifying geometric shapes and sizes.

Hope this helps. Happy learning!

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Problem 1

Draw a straight line and plot X anywhere on it.

Use your compass to trace out a circle with radius 1.5 cm. The circle intersects the line at two points. Let's make Y one of those points.

Also from point X, draw a circle of radius 2.5

This second circle will intersect another circle of radius 3.5 and this third circle is centered at point Z.

Check out the diagram below to see what I mean.

=====================================================

Problem 2

Draw a straight line and plot L anywhere on it.

Adjust your compass to 4 cm in width. Draw a circle around point L.

This circle crosses the line at two spots. Focus on one of those spots and call it M.

Draw another circle centered at point M. Keep the radius at 4 cm.

The two circles intersect at two points. Focus on one of the points and call it N.

The last step is to connect L, M and N to form the equilateral triangle.

See the image below.

=====================================================

Problem 3

I'm not sure how to do this using a compass and straightedge. I used GeoGebra to make the figure below instead. It's a free graphing and geometry program which is very useful. I used the same app to make the drawings for problem 1 and problem 2 earlier.