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Transcript
SIMILAR TRIANGLES Unit 8: Activity 18 SIMILAR TRIANGLES Date Learning Target 1/3 Dilations 1/4 Dilations off the Coordinate Plane 1/5 Similarity Criteria Page # 98 100 102 SIMILAR TRIANGLES Learning Task: I will develop criteria for triangle similarity. SIMILAR TRIANGLES Similar Figures Figures that have the same shape, but not necessarily the same size. When two figures are similar, the ratios of the lengths of their corresponding sides are equal. SIMILAR TRIANGLES ΔABC ∼ ΔPQR ∠A ≅ ∠P ∠B ≅ ∠Q ∠C ≅ ∠R AB BC CA = = PQ QR RP SIMILAR TRIANGLES AA Similarity Postulate If two angles of one triangle are congruent to two angles of another, then the triangles are similar. SSS Similarity Theorem If the lengths of the corresponding sides of two triangles are proportional, then the triangles must be similar. SIMILAR TRIANGLES SAS Similarity Theorem If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides including these angles are proportional, then the triangles must be similar SIMILAR TRIANGLES Quick Write, p. 100… 1) Compare the SAS Congruency Theorem with the SAS Similarity Theorem. 2) Compare the SSS Congruency Theorem with the SSS Similarity Theorem. SIMILAR TRIANGLES Date Learning Target 1/3 1/4 1/5 1/10 Dilations Dilations off the Coordinate Plane Similarity Criteria Using Similarity Criteria Page # 98 100 102 104 SIMILAR TRIANGLES Learning Task: I will apply the similarity criteria in triangles to find unknown sides. SIMILAR TRIANGLES Quick Write, p. 100… 1) Are all right isosceles triangles similar? Explain. 2) Are all equilateral triangles similar? Explain. SIMILAR TRIANGLES Indirect Measurement - Technique that does not use a measurement tool to measure an unknown length. SIMILAR TRIANGLES Quick Write, p. 100… Suggest a reasonable method for approximating the height of a tree. SIMILAR TRIANGLES 5 ft. 39 ft. 11 ft. SIMILAR TRIANGLES SIMILAR TRIANGLES x 21 m 24 m 56 m SIMILAR TRIANGLES Date Learning Target 1/3 1/4 1/5 1/10 1/12 Dilations Dilations off the Coordinate Plane Similarity Criteria Using Similarity Criteria Triangle Proportionality Theorem Page # 98 100 102 104 106 SIMILAR TRIANGLES Learning Task: I will apply the Triangle Proportionality Theorem and it’s converse. SIMILAR TRIANGLES Warm-up, p. 106… Name all the angle pairs. SIMILAR TRIANGLES TRIANGLE PROPORTIONALITY THEOREM If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally. SIMILAR TRIANGLES BD BE = DA EC SIMILAR TRIANGLES Find the value of “x”… SIMILAR TRIANGLES Given that BC is parallel to DE, Find the value of “x”… SIMILAR TRIANGLES PARALLEL LINES & PROPORTIONALITY If three or more parallel lines intersect two transversals, then they divide the transversals proportionally. SIMILAR TRIANGLES AB DE = BC EF SIMILAR TRIANGLES TRIANGLE ANGLE BISECTOR THEOREM An angle bisector of an angle of a triangle divides the opposite side in two segments that are proportional to the other two sides of the triangle. SIMILAR TRIANGLES BD CD = AB AC SIMILAR TRIANGLES
