Constructing triangles: sides and angles

The Maths Habit

Draw all the points that are 2 cm from P.

P2 cm

A circle, radius 2 cm

Construct triangle PQR with PQ = 6 cm, PR = 4 cm and QR = 5 cm.

PQR4 cm5 cm

Arcs of 4 cm from P and 5 cm from Q

Sam measures this angle with a protractor and says it is 130°. Is Sam right?

?0180101702016030150401405013060120701108010090901008011070120601305014040150301602017010180050°

No. It is less than a right angle, so it is acute: 50°. Sam read the wrong scale.

Protractor
A tool for measuring and drawing angles.
Included angle
The angle between two given sides.
Base
The side you draw first.

Two sides and the angle between (SAS)

  1. Draw the base.
  2. Measure the angle at one end and draw a line.
  3. Measure the second side along that line.
  4. Join.
AB7 cm50°5 cmC01801017020160301504014050130601207011080100909010080110701206013050140401503016020170101800

Construct triangle ABC with AB = 7 cm, angle A = 50° and AC = 5 cm. Base, angle, side, join

AB50°C5 cm

Construct triangle DEF with DE = 8 cm, angle D = 40° and DF = 6 cm. The angle line is drawn. Measure 6 cm along the line

DE40°F6 cm

Construct triangle ABC with AB = 7 cm, angle A = 50° and AC = 5 cm. Base, angle, side, join

AB50°C5 cm

Construct triangle GHJ with GH = 6 cm, angle G = 65° and GJ = 4.5 cm. Base, angle, side, join

GH65°J4.5 cm

  1. Construct triangle PQR with PQ = 6 cm, angle P = 70° and PR = 4 cm. Measure QR.

    6 cm

  2. Construct triangle XYZ with XY = 5 cm, angle Y = 120° and YZ = 3 cm. Measure XZ.

    7 cm

AB is 7 cm. Angle A is 45° and angle B is 60°. How do you find C?

Draw both angles. C is where the two lines cross.

A side and two angles (ASA)

  1. Draw the base.
  2. Measure the angle at one end and draw a line.
  3. Measure the angle at the other end and draw a line.
  4. The lines cross at the third corner.
AB7 cm45°60°C01801017020160301504014050130601207011080100909010080110701206013050140401503016020170101800

Construct triangle STU with ST = 7 cm, angle S = 45° and angle T = 60°. Measure SU. SU = 6.3 cm

ST45°60°U

Construct triangle XYZ with XY = 8 cm, angle X = 35° and angle Y = 75°. Measure angle Z. Angle Z = 70°

XY35°75°Z

Construct triangle STU with ST = 7 cm, angle S = 45° and angle T = 60°. Measure SU. SU = 6.3 cm

ST45°60°U

Construct triangle ABC with AB = 5.5 cm, angle A = 70° and angle B = 50°. Measure AC. AC = 4.9 cm

AB70°50°C

Construct triangle STU with ST = 7 cm, angle S = 45° and angle T = 60°. Measure SU. SU = 6.3 cm

ST45°60°U

Construct triangle DEF with DE = 5.5 cm, angle D = 40° and DF = 4 cm. Measure EF. EF = 3.5 cm

DE40°F4 cm

Construct triangle STU with ST = 7 cm, angle S = 45° and angle T = 60°. Measure SU. SU = 6.3 cm

ST45°60°U

Construct triangle KLM with KL = 6 cm, angle K = 55° and angle L = 40°. Measure angle M. Angle M = 85°

KL55°40°M

Construct triangle STU with ST = 7 cm, angle S = 45° and angle T = 60°. Measure SU. SU = 6.3 cm

ST45°60°U

Construct triangle XYZ with XY = 3.5 cm, angle X = 110° and angle Y = 35°. Measure YZ. YZ = 5.7 cm

XY110°35°Z

Constructing triangles: sides and angles worksheet, page 1

Constructing triangles: sides and angles worksheet, page 2

Answer sheet

Thumbs up if it is right. Thumbs down if it is wrong.

  1. For SAS, the angle is the one between the two sides.

    Right

  2. Angles of 100° and 90° at the ends of a side make a triangle.

    Wrong: 190°

  3. ASA triangles drawn by two people come out the same.

    Right

  4. A 50° angle can be read as 130° on the other scale.

    Right

  1. A sail has edges of 4 m and 3 m with 75° between them. Scale 1 cm to 1 m. How long is the third edge?

    4.3 m

  2. Construct a parallelogram with sides 6 cm and 4 cm and an angle of 65°. Measure the longer diagonal.

    8.5 cm

  3. Can you construct a triangle with angle A = 100° and angle B = 85°? Explain.

    No: over 180°

  1. AB = 4 cm. Construct ABC with angle A = 50° and AC = 3 cm.

    Angle 50° at A, then 3 cm along it
    AB4 cm

  2. ASA: what do you draw after the base?

    Both angles: the lines cross at the third corner

  3. Angles of 110° and 75° at the ends of a side: a triangle? Explain.

    No, they add to 185°, more than 180°
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