4a. What is the converse of the Pythagorean Theorem? State it here. b. Use the Law...
Show all work please!!! 9) Prove the converse of the Pythagorean theorem: If the three sides satisfy a2 + b2 = c2 then the triangle is a right triangle.
The only ideas that can be used include: area ABCI-RA2(A+B+C-lpi), the Pythagorean theorem: Cos c cos a cos b. Vectors-dot product cross product, sin A-sin a/sin c; cos A-cos a sin b/sin c; spherical law of sines, spherical law of cosines for sides and spherical law of cosines for angles Let r be the radius of the incircle of triangle ABC on the unit sphere S. If all the angles in triangle ABC are right angles, what is the exact...
NOTE: Please do not copy paste already existing answers. Q) Q) Prove the Converse to the Similar Triangles Theorem (Theorem 5.3.4) Theorem 5.3.4 (Converse to Similar Triangles Theorem). If△ABC and △DEF are two triangles such that AB/ DE = AC/ DF = BC/ EF, then △ABC ~ △DEF. Prove the following Angle-Side-Angle criterion for similarity: If AABC and ADEF are two triangles such that LCA B-LFDE, LABC-LDEF, and DE = r . AB, then AABCADEF with common ratio r Prove...
Activity 7: Right or Not? Develop or reinforce the Pythagorean theorem and its converse and explore the relationship between the lengths of the sides of a triangle and its classification as acute, right, or obtuse Online: Centimeter Graph Paper Other: Scissors PURPOSE MATERIALS Work individually or in pairs. GROUPING From a sheet of graph paper, cut out squares with areas 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and 169 square centimeters. Use three squares to construct a...
2. The triple (a, b, c) is called a Pythagorean triple if a, b and c are natural numbers (in other words, they belong to N) and a2 +bc2. Prove that if a rectangle has sides of rational lengths p and q then the length of its diagonal is irrational if and only if there is a natural number r such that (p,q,r) is a a Pythagorean triple. State clearly any theorem proved in class that you use.
Proof of Pythagorean Theorem Write a proof of the Pythagorean Theorem (a^2+b^2=c^2). Your target audience consists of developmentally-typical 14-year-olds children. They have learned how to calculate areas of rectangles and right triangles, but haven't confidently memorized the formulas. They can follow basic algebra. Feel free to use simple diagrams.
1. a) Prove: if and , then b) State the converse above, and find a counterexample to the converse above. We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
This is 2(b): The following exercise shows that the converse to Lagrange's theorem is false, i.e. even if d ||G|, there need not be a subgroup of G with order d. (a) Let n > 4 and consider the alternating group An. Suppose that NC An is a normal subgroup and that there is a 3-cycle (abc) E N. Prove that N = An. Hint: it is enough to show that N contains all 3-cycles. What is the conjugate of...
Use the Pythagorean Theorem to find the missing side of the triangle. Round to the nearest tenth, if necessary.a = ?, b = 5, c = 8 A. 6.0 B. 6.1 C. 6.2 D. 6.3
(a) Using the Pythagorean Theorem, we can state that Show that d)d) and (b) We need the potential energy of the marble. This is due entirely to gravity, so U=mgy + C to be such that U-0 when ф 0. where we can choose C to be anything that makes our lives easier. We want What is C? Show that with this choice, 4b (using the expression for s found in (a).)