Translating Triangles in the Coordinate Plane

Transcription

1 hapter Summar Ke Terms transformation congruent line segments (71) () image congruent (71) angles () translation corresponding (71) sides () rotation corresponding (73) angles () SSS ongruence Theorem (3) angle included of rotation angle (3) (73) point SS ongruence of rotation (73) Theorem (3) reflection included side (7) () reflection S ongruence line (7) Theorem () S ongruence Theorem () Translating Triangles in the oordinate Plane To translate a triangle in the coordinate plane means to move or slide the triangle to a new location without rotating it Triangle has been translated 1 units to the left and units down to create triangle 999 ' ' ' 11 arnegie Learning The coordinates of triangle are (, ), (7, 5), and (, 5) The coordinates of triangle 999 are 9(, ), 9(3, 3), and 9(, 3) hapter Summar 71

2 Rotating Triangles in the oordinate Plane To rotate a triangle in the coordinate plane means to turn the triangle either clockwise or counterclockwise about a fied point, which is usuall the origin To determine the new coordinates of a point after a 9 counterclockwise rotation, change the sign of the -coordinate of the original point and then switch the -coordinate and the -coordinate To determine the new coordinates of a point after a 1 rotation, change the signs of the -coordinate and the -coordinate of the original point Triangle has been rotated 1 counterclockwise about the origin to create triangle 999 ' ' ' The coordinates of triangle are (, ), (7, 5), and (, 5) The coordinates of triangle 999 are 9(, ), 9(7, 5), and 9(, 5) 11 arnegie Learning 7 hapter ongruence of Triangles

3 Reflecting Triangles on a oordinate Plane To reflect a triangle on a coordinate plane means to mirror the triangle across a line of reflection to create a new triangle Each point in the new triangle will be the same distance from the line of reflection as the corresponding point in the original triangle To determine the coordinates of a point after a reflection across the -ais, change the sign of the -coordinate in the original point To determine the coordinates of a point after a reflection across the -ais, change the sign of the -coordinate in the original point Triangle has been reflected across the -ais to create triangle 999 ' ' ' The coordinates of triangle are (, ), (7, 5), and (, 5) 11 arnegie Learning The coordinates of triangle 999 are 9(, ), 9(7, 5), and 9(, 5) hapter Summar 73

4 Identifing orresponding Sides and ngles of ongruent Triangles ongruent figures are figures that are the same size and the same shape ongruent triangles are triangles that are the same size and the same shape ongruent line segments are line segments that are equal in length ongruent angles are angles that are equal in measure In congruent figures, the corresponding angles are congruent and the corresponding sides are congruent Triangle DEF has been reflected across the -ais to create triangle PQR Line segment DE corresponds to line segment PQ, which means DE PQ Line segment EF corresponds to line segment QR, which means EF QR Line segment DF corresponds to line segment PR, which means DF PR ngle D corresponds to angle P, which means /D /P ngle E corresponds to angle Q, which means /E /Q ngle F corresponds to angle R, which means /F /R The congruence statement for these two congruent triangles is DEF PQR Q E R P D F 11 arnegie Learning 7 hapter ongruence of Triangles

5 Using the SSS ongruence Theorem to Identif ongruent Triangles The Side-Side-Side (SSS) ongruence Theorem states that if three sides of one triangle are congruent to the corresponding sides of another triangle, then the triangles are congruent ccording to the SSS ongruence Theorem, MNP XYZ because MN XY, NP YZ, and MP XZ N X 7 ft 1 ft 1 ft P Z 1 ft 1 ft 7 ft M Y Using the SS ongruence Theorem to Identif ongruent Triangle The Side-ngle-Side (SS) ongruence Theorem states that if two sides and the included angle of one triangle are congruent to the corresponding two sides and the included angle of a second triangle, then the triangles are congruent n included angle is the angle formed b two sides of a triangle 11 arnegie Learning ccording to the SS ongruence Theorem, HGF because HG, GF, and their corresponding included angles, / and /G, are congruent 5 in H 5 in 1 in F 1 in G hapter Summar 75

6 Using the S ongruence Theorem to Identif ongruent Triangles The ngle-side-ngle (S) ongruence Theorem states that if two angles and the included side of one triangle are congruent to the corresponding two angles and the included side of another triangle, then the triangles are congruent n included side is the line segment between two angles of a triangle ccording to the S ongruence Theorem, RST XYW because /S /Y, /T /W, and their corresponding included sides, ST and WY, are congruent R W o m S o m T X Y Using the S ongruence Theorem to Identif ongruent Triangles The ngle-ngle-side (S) ongruence Theorem states that if two angles and the non-included side of one triangle are congruent to the corresponding two angles and the non-included side of a second triangle, then the triangles are congruent ccording to the S ongruence Theorem, RPQ because / /R, / /P, and their corresponding non-included sides, and RQ, are congruent o P 7 o 11 arnegie Learning 9 d o R 9 d 7 o Q 7 hapter ongruence of Triangles