...parallel to the third side. Hint. — Show that this line coincides with a line drawn as in § 129. 131. Exercise. — A straight line joining the middle points of two sides of a triangle equals half the third side. Hint.— Prove DE=BX, and DE-=XC. 132. Dcfs. — A trapezoid is a quadrilateral,...

...third side. Hint.—Show that this line coincides with a line drawn as in § 129. 131. Exercise.—A straight line joining the middle points of two sides of a triangle equals half the third side. Hint.—Vrovz DE=BX, and DE—XC. 132. Dcfs.—A trapezoid is a quadrilateral,...

...equal in area ; and equal triangles on the same base are between the same parallels. Shew that the straight line joining the middle points of two sides of a triangle is parallel to the third side. 2. Draw a tangent to a circle from a given point without its circumference. Shew that two tangents...

...is a right bisector, (X is Y) Therefore the right bisector is the median. ( Y is X) 124. THEO. The line joining the middle points of two sides of a triangle is parallel to the third side. 125. THEO. Converse of § 124. 126. THEO. The line o/§ 124 is equal to one half the third side. 127....

...the points are taken does . ,; .not affect the result. ^<--- - . t 43. Prove analytically that the line joining the middle points of two sides of a triangle is parallel to the third side ; and equal to one half of it. • ]fS^S"' I •+• , . , * .- /* ', s \ THE POINT. 21 45. Prove analytically...

.../\ side. M/ \N Hint. — Show that this line coincides with a line drawn / J^ as in §127. A < 129. Exercise. — A straight line joining the middle points of two sides of a triangle is equal to half the third / side. * ty— Hint.— Prove DE = BX, and DE = XC. p/ , 130. Defs. — A...

...assumes only Euclid, I. 43, and its converse, with the well-known deductions, " the line joining the mid points of two sides of a triangle is parallel to the third side," and " the mid point of one diagonal of a parallelogram is also the mid point of the other." The proof...

...parallel to AC. (Sum of 4 at B = 2 rt. A.) MISCELLANEOUS THEOREMS. PROP. XLVII. THEOREM. 130. 77;e line joining the middle points of two sides of a triangle is parallel to the third side, and equal to one-half of it. B Given line DE joining middle points of sides AB and AC, respectively,...

...square are of equal length, bisect each other, and are at right angles. 10. Prove analytically that the line joining the middle points of two sides of a triangle is parallel to the third side and equal to half its length. 11. Find the locus of the vertex of a triangle whose base is 2 a and...

...whose vertices are (2, '2), (-7, ~1), and (— 1, 5). Plot the figure. 20. Show analytically that the line joining the middle points of two sides of a triangle is half the length of the third side. 21. A point is 7 units distant from the origin and is equidistant...