This problem builds on the students' recent discoveries that similar figures have the same ratio between corresponding side lengths and the same measurements for

corresponding angles; at this point ideas pertaining to the "center of dilation" and "lines of dilation" are brought in.

When nonlinearity criterion was used the value of [G.sub.Ic] of glass/epoxy specimen was by 2.8, 2.76, 1.78 and 2.21 times greater if compared with [G.sub.Ic] values of carbon/epoxy specimen of the

corresponding angles of layer reinforcement in delamination area: 0//0, 0//90, 0//+ 45 and + 45//- 45.

He attempted to prove the proposition, "the

corresponding angles (the degrees of

corresponding angles) formed by two parallel straight lines and a straight line that is not parallel to them are the same" but failed.

They are represented at a tool drawing with

corresponding angles. For proper solution of the cutting tool those angles must have appropriate values dependent on some rules which will ensure effectiveness of the designed cutting tool.

During the remaining sessions, participants explored properties of similar shapes with respect to perspective point, to scale factor, to corresponding sides, to

corresponding angles, and to corresponding distances from the point of projection.

The measurement epochs are recorded together with the

corresponding angles. We use stars with magnitudes between 2 and 6, zenith angles from 20[degrees] to 35[degrees] and azimuths close to meridian or prime vertical.

If students master this concept quickly, then the teacher can continue to accelerate them with eighth-grade concepts, such as exploring the relationship between

corresponding angles in a variety of geometric figures.

That is, I would find two pieces which had

corresponding angles that fit snugly.

The

corresponding angles for the handles on this box ranged from 7[degrees] to 35[degrees] and from 50[degrees] to 83[degrees], respectively.

That is, their

corresponding angles are congruent and their sides are proportional.

In contrast, the

corresponding angles of a perfect octahedron are 180 [degrees], 90 [degrees], and 90 [degrees], and the corresponding distances are 2, 1.41, and 1.41.

For example, in explaining why all of the angles measured 135[degrees], one student wrote (refer to Figure 6): "If angle BDQ is 45 degrees, then angle MQP is 45 degrees, because

corresponding angles are congruent where parallel lines are present (parallel lines are present because of the square)." Two lines later, the student continued: "Now, a trapezoid DQMF exists (DF is parallel to QM, because it is already established that the angles FDQ and DQM are 45 degrees and 135 degrees respectively, and if the same side interior angles are supplementary, then the lines are parallel)." In the first statement, the student essentially assumes the segments are parallel to determine the angle measures.