Chapter 5.5, Problem 42PPS

a.

To determine

Draw three pairs of triangles having two pairs of congruent sides and one pair of non congruent sides.

Answer to Problem 42PPS

  

Explanation of Solution

Given information:

  $\Delta ABCand\Delta DEF,where\overline{AB}\cong \overline{DE}and\overline{AB}\cong \overline{DF}$

Calculation:

Here, by using a ruler and a compass to congruence three pairs of triangles having two pairs of congruent sides and one pair of non congruent sides.

Now, we have:

  $\Delta ABCand\Delta DEF,where\overline{AB}\cong \overline{DE}and\overline{AB}\cong \overline{DF}$

  

Hence, the results are shown in the above figures.

b.

To determine

Measure and record the values of $BC,m\angle A,EFandm\angle D$ .

Answer to Problem 42PPS

  $\begin{array}{lllll}TrianglePair\hfill & BC\hfill & m\angle A\hfill & EF\hfill & m\angle D\hfill \\ 1\hfill & 0.75\hfill & 25\hfill & 2\hfill & 105\hfill \\ 2\hfill & 0.3\hfill & 15\hfill & 1\hfill & 97\hfill \\ 3\hfill & 0.8\hfill & 44\hfill & 1.4\hfill & 101\hfill \end{array}$

Explanation of Solution

Given information:

  $\Delta ABCand\Delta DEF,where\overline{AB}\cong \overline{DE}and\overline{AB}\cong \overline{DF}$

Calculation:

Here, we have to Measure and record the values of $BC,m\angle A,EFandm\angle D$ :

  $\begin{array}{lllll}TrianglePair\hfill & BC\hfill & m\angle A\hfill & EF\hfill & m\angle D\hfill \\ 1\hfill & 0.75\hfill & 25\hfill & 2\hfill & 105\hfill \\ 2\hfill & 0.3\hfill & 15\hfill & 1\hfill & 97\hfill \\ 3\hfill & 0.8\hfill & 44\hfill & 1.4\hfill & 101\hfill \end{array}$

Hence, the results are shown in the above table.

c.

To determine

Prepare the conjecture about the relationship between the angles opposite the non congruent sides of a pair of triangles having two pairs of congruent legs.

Answer to Problem 42PPS

If the two triangles are with two pairs of congruent sides then the angle opposite the longest of the third pair is greater than the angle opposite the shortest of the third pair.

Explanation of Solution

Given information:

  $\Delta ABCand\Delta DEF,where\overline{AB}\cong \overline{DE}and\overline{AB}\cong \overline{DF}$

Calculation:

Here, we will compare $m\angle Aandm\angle D$ :

The angle opposite the longer of the two non congruent sides is greater than the angle opposite the shorter one.

Hence, the conjecture is, if the two triangles are with two pairs of congruent sides then the angle opposite the longest of the third pair is greater than the angle opposite the shortest of the third pair.