* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Geometry CCSS Common Task: Proving Thales` Theorem Name
Survey
Document related concepts
Lie sphere geometry wikipedia , lookup
Steinitz's theorem wikipedia , lookup
Euler angles wikipedia , lookup
Rational trigonometry wikipedia , lookup
Problem of Apollonius wikipedia , lookup
Line (geometry) wikipedia , lookup
History of geometry wikipedia , lookup
Trigonometric functions wikipedia , lookup
Noether's theorem wikipedia , lookup
RiemannβRoch theorem wikipedia , lookup
Four color theorem wikipedia , lookup
Pythagorean theorem wikipedia , lookup
History of trigonometry wikipedia , lookup
Brouwer fixed-point theorem wikipedia , lookup
Transcript
Geometry CCSS Common Task: Proving Thalesβ Theorem Cluster: G.C.A - Understand and apply theorems about circles Name: ________________________________________ Date: ___________________ Thalesβ theorem states the following: If π¨, π©, and πͺ are three distinct points on a circle, and Μ Μ Μ Μ π¨π© is a diameter of the circle, then β π¨πͺπ© is right. Use the challenge below to Prove Thalesβ theorem. a. Draw circle π with distinct points π΄, π΅, and πΆ on the circle and diameter Μ Μ Μ Μ π΄π΅ . Prove that β π΄πΆπ΅ is a right angle. b. Μ Μ Μ Μ ). What types of triangles are β³ π΄ππΆ and β³ π΅ππΆ? How do you know? Draw a third radius (ππΆ c. Using the diagram that you just created, develop a strategy to prove Thalesβ theorem. d. Label the base angles of β³ π΄ππΆ as π° and the base angles of β³ π΅ππΆ as π°. Express the measure of β π΄πΆπ΅ in terms of π° and π°. e. How can the previous conclusion be used to prove that β π΄πΆπ΅ is a right angle? Adapted from the mid-module assessment: https://www.engageny.org/resource/geometry-module-5