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Transcript
Date NOTES CLASSIFYING TRIANGLES CLASSIFYING TRIANGLES BY ANGLES A right triangle An obtuse triangle An acute triangle An equiangular triangle pyy In an acute triangle, CA, k ', In an obtuse triangle the angles are In a right triangle In an equiangular ' 7 angle is angle is triangle, ,_.,i • Scalene Triangle N are CLASSIFYING TRIANGLES BY THEIR SIDES Isosceles Triangle Equilateral Triangle two sides are congruent At least (7,- sides are congruent. ---7 Cl) All congruent sides are . The angle formed by — triangle the two congruent sides are called `ce.c7::: Z.The other two angles are 10 0.3€..- angles. The side Opposite the In an \ the legs is the angles vertex is the Triangle ABC is isosceles A What is the vertex? What sides are legs? _ What side is the base? and Z What angles are base angles? ( CLr C), C011a 7 • t 0 VC, _ 1 Symbols and Definitions in Geometry Symbols save time and space when writing. Here are the most common geometrical symbols: Symbol Meaning Example In Words A Triangle AABC has 3 equal sides Triangle ABC has three equal sides Angle m--ABC is 45° The measure of the angle formed by ABC is 45 degrees. J_ Perpendicular AB-LCD The line AB is perpendicular to line CD II Parallel EF II GH The line EF is parallel to line GH Degrees 360° makes a full circle Right Angle (90 0 ) L. is 90° A right angle is 90 degrees AB The line between A and B AB Line Segment Line "AB" .A1.1 The line that starts at A, goes through B and continues on Ray "AB" Congruent (same AABC ADEF Triangle ABC is congruent to triangle DEF Similar (same shape, different size) ADEF—AMNO Triangle DEF is similar to triangle NINO Therefore a=b ." • b=a a equals b, therefore b equals a Para11 el TOICE5 MN is parallel to CD shape and size) • '4, The infinite line that includes A and The corresponding congruent sides are marked with small straight line segments called hash marks. The corresponding congruent angles are marked with arcs. Conament Angles and Congruent Line Segments ZCAB is congruent to/ FDE ZABC is congruent to ZDEF ZACB is congruent to /DFE ZCAB ZFDE ZABC ZDEF LACB ZDFE AB is congruent toDE AC DF BC is congruent toEF AB DE BC EF AC is congruent toDF 1. Graph AABC using points A(0, -4), B(0, -9) and C(-2, -5). 2. Classify AABC. i I A -------, ! ! 8. I • I 4 1 a. Determine if AABC is scalene, isosceles, or equilateral. Explain your reasoning. . -1.-- . h-1---! 1-I i .—.. , ! 1 --- . L. 1 I b. Determine if AABC is a right triangle. Explain your reasoning. If it is not a right triangle, use a protractor to detei mine what type of triangle it is. C CLASSIFY QUADRILATERALS DEFINITIONS Quadrilateral: Parallelogram: Rectangle: Rhombus: Square: Trapezoid: 2 . g..!. _2i _....1......... _ __J. : 1 . , ,_ i--_ . —I 1 -1 ! ---,---t-- I 1 I I . ! i .., 1 '' 1 1 h 1----, It is given that ABCD is a parallelogram. Graph / lAB CD on the grids provided. Decide whether it is a rectangle, rhombus, square or none of the above. Justify your answer using the definitions of the quadrilaterals. Fill in the answers in the space provided and him in this sheet. 1. Points: A(3, 1), B(3, -3), C(-2, -3), D(-2, 1) SHAPE: Justification 2. Points: A(0, 4), B(6, -2), C(0, -2), D(-6, 4) .. _ SHAPE: .......... ___ .,_rt .. I 1 I I .... ..., i..._v _„....., , v.. v . .... I t . _...... Justification: I L. , _ _ ........ .... , ..... ....._ . ___ ....._ •6 ...... .. ... -..... .... _ ..... - . I. -1.-- . -1--. __LI_ 1 .... I I_ L.... -1—"! i 1 3 3. Points: A(1, 1),B(3, 5), C(5. 1), D(3, -3) SHAPE: _ Justification 4. Points: A(2, 5), B(5, 2), C(2, -1), D(-1, 2) SHAPE: Justification: 4