Exercise 22 Page 370

You need two triangles with two pair of congruent angles and the corresponding included sides to be congruent too.

See solution.

Practice makes perfect

By using a ruler, we will draw the first triangle.

Next, we will measure two angles of the triangle △ ABC and the included side.

If we want to draw a second triangle that is congruent to △ ABC by the Angle-Side-Angle (ASA) Congruence Postulate, we will follow the steps below.

Draw a segment PQ of length 3 cm which will be congruent to AC.
Draw line that passes through P and forms an angle of 80^(∘) with PQ.
Draw a second line that passes through Q and forms an angle of 37^(∘) with PQ. Here, we will obtain the second triangle.

Below we list the corresponding congruent parts. cc ∠ A ≅ ∠ P & Angle AC ≅ PQ & Included Side ∠ C ≅ ∠ Q & Angle As we can see, by the Angle-Side-Angle (ASA) Congruence Postulate we can conclude that △ ABC ≅ △ PRQ.

Hints

Check the answer

Practice exercises

Asses your skill