Question

additional practice problem set
unit 1 lesson 12 additional practice problems

1. a. show that the two pentagons are congruent.

b. find the angle measures of abcde and the side lengths of nmlko.

Explanation:

Step1: Recall congruence criteria

Two polygons are congruent if their corresponding sides and angles are equal. By observing the grid - based figure, we can see that the two pentagons have the same shape and size. We can count the grid - units for side lengths and measure angles (or note the angle measures given for the second pentagon which will be the same for the first due to congruence).

Step2: Identify corresponding parts

For congruent pentagons \(ABCDE\) and \(NMLKO\), we know that \(\angle A=\angle N\), \(\angle B=\angle M\), \(\angle C=\angle L\), \(\angle D=\angle K\), \(\angle E=\angle O\), \(AB = NM\), \(BC=ML\), \(CD = LK\), \(DE=KO\), \(EA=ON\).

Step3: Find angle measures of \(ABCDE\)

The angle measures of \(ABCDE\) are the same as those of \(NMLKO\). So \(\angle A = 135^{\circ}\), \(\angle B=135^{\circ}\), \(\angle C = 71.6^{\circ}\), \(\angle D=108.4^{\circ}\), \(\angle E = 135^{\circ}\).

Step4: Find side lengths of \(NMLKO\)

The side lengths of \(NMLKO\) are the same as those of \(ABCDE\). So \(AB = NM=1\), \(BC = ML = 1.4\), \(CD=LK = 2.8\), \(DE=KO = 2.2\), \(EA=ON = 1.4\).

Answer:

a. The two pentagons are congruent as their corresponding sides and angles are equal (by observing the grid - based figure and noting equal side - lengths and angle - measures).
b. Angle measures of \(ABCDE\): \(\angle A = 135^{\circ}\), \(\angle B=135^{\circ}\), \(\angle C = 71.6^{\circ}\), \(\angle D=108.4^{\circ}\), \(\angle E = 135^{\circ}\). Side lengths of \(NMLKO\): \(NM = 1\), \(ML=1.4\), \(LK = 2.8\), \(KO = 2.2\), \(ON = 1.4\)