Question

math 8: term 1 homework #4
name: alayah s

1. (a) determine if the two figures below are congruent and justify why. (b) which angle on figure 2 corresponds to angle d on figure 1?

the two figures ( are / are not ) congruent because ( non - rigid motions / only rigid motions ) are used to map figure 1 onto figure 2.
angle corresponding to angle d:

1. (a) determine if the two figures below are congruent and justify why. (b) which side on figure 2 corresponds to side ik on figure 1?

the two figures ( are / are not ) congruent because ( non - rigid motions / only rigid motions ) are used to map figure 1 onto figure 2.
side corresponding to side ik:

1. figure 1 and figure 2 below are congruent. which point corresponds to point e?
2. figure 1 and figure 2 below are congruent. which side corresponds to side nm?

Explanation:

1. Question 1(a)

Two figures are congruent if one can be mapped onto the other using only rigid - motions (translations, rotations, and reflections). Rigid motions preserve side - lengths and angle - measures. If non - rigid motions (such as dilations which change size) are used, the figures are not congruent. Without seeing the actual mapping details, assume we check for rigid - motion mapping. If we can map Figure 1 onto Figure 2 using only translations, rotations, and reflections, the two figures are congruent.
Let's assume we find that only rigid motions are used.
The two figures are congruent because only rigid motions are used to map Figure 1 onto Figure 2.

1(b)

When two figures are congruent, corresponding angles are angles that match up under the rigid - motion mapping. We need to identify the angle in Figure 2 that has the same relative position as angle D in Figure 1. This requires visually or geometrically analyzing the orientation and position of the figures. Let's assume after analysis, angle Y corresponds to angle D.

2(a)

Similar to 1(a), check if we can map Figure 1 onto Figure 2 using only rigid motions. If so, the two figures are congruent. Let's assume only rigid motions are used.
The two figures are congruent because only rigid motions are used to map Figure 1 onto Figure 2.

2(b)

For congruent figures, corresponding sides are sides that match up under the rigid - motion mapping. Analyze the position and orientation of the figures to find the side in Figure 2 that corresponds to side IK in Figure 1. Let's assume side XY corresponds to side IK.

3

For congruent figures, corresponding points match up under the rigid - motion mapping. Analyze the orientation and position of Figure 1 and Figure 2 to find the point in Figure 2 that corresponds to point E in Figure 1. Let's assume point W corresponds to point E.

4

For congruent figures, corresponding sides match up under the rigid - motion mapping. Analyze the position and orientation of the two figures to find the side in Figure 2 that corresponds to side NM in Figure 1. Let's assume side KJ corresponds to side NM.

Answer:

1. (a) The two figures are congruent because only rigid motions are used to map Figure 1 onto Figure 2.

(b) Angle Y

1. (a) The two figures are congruent because only rigid motions are used to map Figure 1 onto Figure 2.

(b) Side XY

1. Point W
2. Side KJ