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Construct a Triangle Given the Lengths of Its Three Sides - Constructing a Triangle When the Measures of Two of Its Angles and the Length of the Side Included Between Them is Given. (ASA Criterion)

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Constructing a Triangle When the Measures of Two of Its Angles and the Length of the Side Included Between Them is Given. (ASA Criterion):

Draw a rough sketch. Now, draw the given line segment. Make angles on the two ends.

1) Construct ∆XYZ if it is given that XY = 6 cm, m∠ZXY = 30° and m∠XYZ = 100°.

Step 1: Before actual construction, we draw a rough sketch with measures marked on it.

Step 2: Draw XY of length 6 cm.

Step 3: At X, draw a ray XP making an angle of 30° with XY. By the given condition Z must be somewhere on the XP.

Step 4: At Y, draw a ray YQ making an angle of 100° with YX. By the given condition, Z must be on the ray YQ also.

Step 5: Z has to lie on both the rays XP and YQ. So, the point of intersection of the two rays is Z.

∆XYZ is now completed.

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