Question

Given: YZ is the base of an isosceles triangle. Prove: XA bisects. Given: CE = CF. Prove: CDG is isosceles. Given: HJ = MKJ. Conclusion: JOK is isosceles. Given: PSV is equilateral, R is the midpt. of SP, T is the midpt. of SV. RT = 1/2 SV.

A. Corresponding angles
B. Parallel lines
C. Isosceles triangles
D. Midpoint theorem

Answer 1

This answer covers geometric properties and theorems, notably the Pythagorean theorem, the characteristics of isosceles triangles, and the midpoint theorem in equilateral triangles.

Step-by-step explanation:

The information provided refers to various geometric properties and theorems including the Pythagorean theorem, characteristics of isosceles triangles, and the properties of equilateral triangles and their midpoints. The Pythagorean theorem formula, a² + b² = c², is used to relate the sides of a right triangle, where 'a' and 'b' are the legs of the triangle and 'c' is the hypotenuse.

When applying this theorem, we can calculate the length of one side of a triangle when the lengths of the other two are known. For isosceles triangles, certain properties are used to understand the relations between sides and angles. Lastly, the midpoint theorem in equilateral triangles helps determine the lengths and properties of line segments connecting midpoints of sides.