Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Euler angles wikipedia , lookup
Golden ratio wikipedia , lookup
Noether's theorem wikipedia , lookup
Rational trigonometry wikipedia , lookup
Trigonometric functions wikipedia , lookup
Reuleaux triangle wikipedia , lookup
Brouwer fixed-point theorem wikipedia , lookup
History of trigonometry wikipedia , lookup
Four color theorem wikipedia , lookup
Euclidean geometry wikipedia , lookup
Name: _________________________________________________________ Date: ______________ Per: _______ LC Math 2 Adv โ Isosceles Triangle Theorem (LT 2) Part 1 โ Construction What must be constructed to form an isosceles triangle? Use your compass and straightedge to construct an isosceles triangle in the space below. Along with your partner, use inductive reasoning to make a postulate about isosceles triangles. Explain below. Part 2 โ Transformations Britney proposes an argument for why ๐โ ๐ต must equal ๐โ ๐ถ. She says: โIf I draw the bisector of โ A then this is a line of symmetry for โณABC and so m(โ B)=m(โ C).โ a) What additional information is provided when you draw the bisector of โ A? b) How can you add to Britneyโs argument to make it more complete? Write a full explanation of her reasoning process below. c) If the two triangles formed in Britneyโs argument can be mapped onto one another using a sequence of isometries, what conclusion can be drawn? Part 3 โ Proof Isosceles Triangle Theorem: If two sides of a triangle are congruent, then the angles opposite those sides are congruent. Use the understanding from Britneyโs reasoning to complete a proof of the Isosceles Triangle Theorem. Given: ฬ ฬ ฬ ฬ ๐ด๐ต โ ฬ ฬ ฬ ฬ ๐ด๐ถ Prove: โ ๐ต โ โ ๐ถ Statement Reason Part 4 โ Proof of the Converse Converse of the Isosceles Triangle Theorem: If two angles of a triangle are congruent, then the sides opposite those angles are congruent. Use the understanding from Britneyโs reasoning to complete a proof of the Converse of the Isosceles Triangle Theorem. Given: โ ๐ โ โ ๐ ฬ ฬ ฬ ฬ ฬ ฬ ฬ ฬ โ ๐ ๐ Prove: ๐ ๐ Statement Reason