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Draw Geometric Shapes with Given Conditions

Students draw triangles and other polygons with specified side lengths and angle measures using a ruler, protractor, and/or technology. They determine when the given conditions produce a unique shape, more than one shape, or no shape at all.

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Draw Geometric Shapes with Given Conditions

Grade 7 · Geometry · question 1 of 3

0 of 20

20 rungs. A star at the top.

+3+4012345

Sides 3 and 4: the third side is longer than ___

Both sides are laid from 0. How far apart do their ends land?

How it is taught

0:00 of 3:46

Three lengths make a triangle only if each pair sums to more than the third.

That test is the triangle inequality.

Read it: Triangles from given parts

A triangle has angles of 65° and 75°. Its 3 angles add to 180°: 65 + 75 = 140, so the third angle is 180 − 140 = 40°.

  1. Add the angles you know.
  2. Subtract that sum from 180° for the third angle.
  3. For 3 side lengths, check that the 2 shorter sides add to more than the longest.

Tear off a triangle's 3 corners and they line up along a straight line, 180°.

Sides 2, 3 and 6 cannot meet: 2 + 3 = 5, less than 6, so the short sides cannot reach each other.

Sides 4, 5 and 6 do make a triangle: 4 + 5 is more than 6.

A triangle's angles add to 180°, and its 2 shorter sides add to more than its longest.

Subtracting from 360: 360 − 140 = 220.

A triangle's angles add to 180°, not 360°: 180 − 140 = 40.

Two angles of a triangle are 25° and 105°. How many degrees is the third angle? — 50. The angles add to 180°: 180 − 25 − 105 = 50.

Triangle with sides 3 cm, 4 cm, 5 cm

Can we draw a triangle with sides three, four, and five centimeters? Let's find out!

Start with the longest side. Draw five centimeters and label the ends A and B.

From A, swing an arc with radius three — every point on it is exactly three centimeters from A.

From B, swing an arc with radius four — every point is four centimeters from B.

Where the two arcs cross is our third vertex. Call it C.

Connect A to C and B to C. We have our triangle!

Let's measure the angle at C with a protractor.

Look at the square corner. It's exactly ninety degrees — a right triangle!

Grade 7 · Building triangles with a ruler and compass

Any triangle built from these three sides will look just like this one. Three side lengths give one unique shape.

Sides three, four, and five make one and only one triangle — and it's a right triangle!

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
Climbing now
Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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