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Download TRI 01 Worksheet HW 28 Name_____________ Geometry 2013
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Transcript
TRI 01 Worksheet HW 28 Geometry 2013 Name_____________ Triangles can be classified by both their ANGLES and by the relative lengths of their SIDES. Complete the table with classification criteria: Classifications (by angles) Acute Obtuse If the Largest Angle between ____ º & ___ º is______, then the triangle less than ___ º …acute. …obtuse is… Example: 97º 27º 80º 73º Right exactly =___ º …right 50º 10º 73º 90º 40º Now classify the following triangles in terms of angles only. 1) In Geometry, we are NEVER allowed to guess at an angle’s measure (we don’t assume without evidence). However, pretend that rule doesn’t apply for just a moment. Based upon the picture, classify the triangles below: ________________ _____________ _________________ _____________ 2) Now, use good Geometry skills to deduce the angle classification of each triangle below. (Remember, the sum of the interior angles in any triangle add up to 180º.) 105º 20º ??º 90º 70º ______________ ??º 60º 10º 60º 80º 60º 100º _______________ ________________ ______________ ________________ Equilateral Isosceles all three at least 2 …equilateral …isosceles Classifications (by sides) A triangle with _______ congruent sides is called…. Scalene NO …scalene Now classify the following triangles in terms of sides only. 3) In Geometry, we are NEVER allowed to guess at a side’s length (we don’t assume without evidence). However, pretend that rule doesn’t apply. Based upon the picture, classify the triangles below: ________________ _____________ _________________ _____________ 4) Now, use good Geometry skills to deduce the side length classification of each triangle below. 3 4 2 5 ______________ 4 8 8 8 6 8 6 ?? ______________* ________________ ______________ ________________ * notice anything? 5) Now classify the following triangles by BOTH angles AND side length (say Angle then Side) 3 53º 90º 80º 4 37º 5 _______ ______ 50º ??º ??º 50º _______ _______ 60º 60º _______ _______ 10º ??º 60º _______ _______ 10º ??º _______*_______ Geometry HW 28 Name: __________________ TRI Unit Period: _____ Date________ TRI01: Define and classify triangles by sides and angles. Classify each triangle below by both sides and angles. 5cm 80 30 70 3cm 90 8 ft 4cm 60 60 45 45 100 18 ft By angle => By side => Sketch a triangle, including appropriate marks or labels to match the following classifications: 1) acute, isosceles 2) obtuse scalene TRI02: Fill in the missing steps for the following proof of the Triangle Angle Sum Theorem. 8 ft Unit 5: TRI - Triangles: Attributes, Congruence and Proof SKILL DESCRIPTION TRI 01 Define and classify triangles by sides and angles. TRI 02 Fill in the missing statements/reasons in a 2 column proof of the Triangle Angle Sum Theorem. TRI 03 Given two angles of a triangle, find the third. Given algebraic expressions for the three angles in a triangle, solve for x and find the measure of each angle. TRI 04 State the corollaries to the Triangle Angle Sum Theorem a) In a triangle, no more than one angle can be greater than or equal to 90 degrees. (this is a proof by contradiction). b) In a right triangle, the two non-right angles are complementary. c) If two angles of one triangle are congruent to two angles of another, then the third angles are also congruent. TRI 05 State and apply the Remote Interior Angles Theorem (aka Exterior Angle Theorem). Solve problems, given exterior and remote interior angles, using algebra. TRI 06 Define polygon congruence. TRI 07 Given two polygons, determine if they are congruent by the Definition of Polygon Congruence. TRI 08 Given two congruent polygons (especially triangles), write polygon congruence statement and identify congruent corresponding parts. TRI 09 Use SSS, SAS, ASA, AAS to determine if 2 triangles are congruent. TRI 10 Be able to distinguish ASS from RHL, and use RHL to determine if two triangles are congruent. TRI 11 Write two column proofs to establish simple triangle congruence. TRI 12 Write simple triangle congruence proofs in a Flow Proof format. TRI 13 Write two column or flow proofs for more complicated triangle congruence (including Reflexive, Symmetric, Parallel Lines, Vertical Angles, CPCTC, etc.). TRI 14 Apply the concepts of Isosceles Triangle Theorem and its Converse in solving algebraic equations. TRI 15 Prove Isosceles Triangle Theorem in each of four ways: Given an isosceles triangle and ONE of the following: altitude, angle bisector or median, prove that base angles are congruent. TRI 16 Prove the Converse of the Isosceles Triangle Theorem. TRI 17 Use Triangle Inequality Theorem to determine if three given sides form a triangle. Also be able to determine the range of values for a third side, given the other two. TRI 18 Given two angles in a scalene triangle, list the triangle’s side lengths in descending order and vice versa. TRI 50 Given a triangle and designated parts, construct significant segments. TRI 99 a) Given a triangle and a designated vertex, construct the median. b) Given a triangle and a designated vertex, construct the altitude. c) Given a triangle and a designated vertex, construct the angle bisector. d) Given a triangle & a designated side, construct perpendicular bisector. Solve problems you haven’t seen before, using analysis and synthesis of the information learned so far.