The student is wrong. We could measure an angle because it doesn't matter how long the two rays are. We could put two points A and B on the two rays, and the angle doesn't change. The angle between the 2 rays is same as the angle AOB, which it could be measured with a protractor.

In geometry, two figures are congruent if they have the same shape and size, but are in different positions (for instance one may be rotated, flipped, or simply placed somewhere else).
For example, two angles ABC and DFE, say, are "equal" if and only if there are exactly the same angle: that would mean that B and F are just different ways of referring to the same point and that A is on one of the rays FD or FE and C is on the other one.

Two angles are "congruent" if and only if they have the same measure.

Generally speaking, in mathematics, we use the term "equal" to mean "(possibly different) ways of ...

Solution Summary

The expert finds the sides of similar triangles. The points when angles two are located.

... ABO, < A = 45 degrees and <B = 45 degrees and in the triangle CAD, <A=45 ... Since the angles are in same measure, the two triangles ABO and CAD are similar. ...

Congruent and similar triangles. ... of two of the sides as 100 m and 80 m. When the architect began the design on drafting paper, she drew a triangle to scale with ...

... In this solution we investigate Triangles, Bisectors and Midpoints. ... So we know EF is parallel to BC. So we get triangle ANE is similar to triangle AMC. ...

... Two similar triangles will have the same angles, but may have different sides. For example, a right triangle with side lengths 3-4- 5 is similar to a right ...

... If they are the same then BDE is an isosceles triangle, and with knowing the ... org or anywhere on the web for more details) Because of similar triangles (1.8 is ...

... 6. Again, we are dealing with similar triangles. However, we are asked about the area of illumination. ... 7. Again, this is similar triangles problem. ...

... Because the triangles are similar, if you make ratios using the length of the side of one triangle as the numerator and the length of the corresponding side of ...

... rectangle (b) one example is one pair of lines which encloses an area (c) one example is two similar triangles 98. (a) the sum of angels in a triangle is more ...