The Ontario High School Geometry Theoretical

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ABC is a A in which BC 2 = AB 2 + AC 2 . To prove that L A is a rt. /_.
Construction. Make a rt. L D and cut off DE = AB, DF = AC Join EF.
BC 2 = AB 2 + AC 2 (Hyp. ) = DE 2 -f DF 2 = EF 2 (V D is a rt. /_). (1113, p. 122. ) .. BC = EF.
IAB - DE, AC- DF, BC = EF, . '. L A = L D. (14, p. 22. ) . '. L A is a rt. L.
128 THEORETICAL GEOMETRY BOOK II 84. Exercises 1. The sides of a A are 3 in. , 4 in. And 5 in. Prove that it is a rt. - L. D A.
2. The sides of a A are 13 mm. , 84 mm. And 85 mm. Prove
...that it is a rt. - L d A.
3. In the quadrilateral ABCD, AB 2 -f CD 2 = BC 2 + AD 2 . Prove that the diagonals AC, BD cut at rt. L. S.
4. If the sq. On one side of a A be less than the sum of. The squares on the other two sides, the L contained by these sides is an acute L . (Converse of 83, Ex. 28. ) 5. State and prove a converse of 83, Ex. 29.
6. Using a tape-measure, or a knotted cord, and Ex. 1, draw a st. Line at rt. L s to a given st. Line.
7. Show that, if the sides of a A are represented by m?


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