3 Ways To Prove Triangles Are Similar SAS Postulate SSS .
GSE GeometrySimilarityNotesName: Block:3 Ways to Prove Triangles are SimilarAA Postulate:If two angles of one triangleare congruent to two anglesof another, then the trianglesare similar.SAS Postulate:If one angle of one triangle iscongruent to the one angle ofanother triangle and theadjacent sides areproportional, then thetriangles are similar.SSS Postulate:If all three sides of onetriangle are proportional tocorresponding sides ofanother triangle, then thetriangles are similar.You can mark vertical angles and shared angles congruent!Explain why the triangles are similar (SSS , SAS , or AA ) and write a similaritystatement.1. ๐ ๐๐ ๐๐ฆ2. ๐ป๐ฝ๐บ ๐๐ฆ3. ๐ด๐ต๐ถ ๐๐ฆ4. ๐ด๐ธ๐ท ๐๐ฆ5. ๐๐๐ ๐๐ฆ6. ๐๐๐ ๐๐ฆ7. ๐บ๐๐พ ๐๐ฆ8. ๐ด๐ต๐ถ ๐๐ฆ
GSE GeometrySimilarityNotesSolve for the missing lengths of the similar figures.9.10.Similar Triangle Word Problems.11. A tree 24 feet tall casts a shadow 12 feetlong. Brad is 6 feet tall. How long is Brad'sshadow?12. A 40-foot flagpole casts a 25-foot shadow.Find the height of a building that casts a 125foot shadow.Explain why the triangles are similar (SSS , SAS , or AA ) and find each length13. Similar by and CE 14. Similar by and RQ 15. Similar by and GK 16. Similar by and SV
GSE GeometrySimilarityNotesTriangle Proportionality TheoremTriangle Proportionality Theorem- If a line parallel to one side of a triangle and intersects theother two sides of the triangle, then it divides the two sides proportionally.ฬ ฬ ฬ ฬ ฬ ฬ ฬ ฬ ฬ ๐กโ๐๐๐๐๐๐๐๐ท๐ธ ๐ต๐ถ๐ด๐ท ๐ด๐ธ ๐ท๐ต ๐ธ๐ถEx.1 Solve for x.Ex.2 Solve for x.Ex.3 Solve for x.Ex.4 Find the value of x if SR is parallel toPQ.ฬ ฬ ฬ ฬ ฬ ฬ ฬ ๐ฝ๐ฬ ฬ ฬ .Ex.5 Determine whether ๐พ๐ฬ ฬ ฬ ฬ ฬ ฬ ฬ ๐ฝ๐ฬ ฬ ฬ .Ex.6 Determine whether ๐พ๐
GSE GeometrySimilarityNotesTriangle Bisector TheoremTriangle Bisector Theorem- if one angle of a triangle is bisected, or cut in half, then the anglebisector of the triangle divides the opposite side of the triangle into two segments that areproportional to the other two sides of the triangle.๐ถ๐ด ๐ต๐ด ๐ถ๐ ๐ต๐Ex.1 Solve for x.Ex.2 Solve for p.Ex.3 Solve for x.Ex.4 Traingle Proportionality Theorem. Find xand y.
GSE GeometrySimilarityNotesMidsegmentsTriangle Midsegment Theorem โ If a segment joins the midpoints of two sides of a triangle, thenthe segment is parallel to the 3rd side and half its length.1ฬ ฬ ฬ ฬ ฬ ฬ ฬ ฬ ๐๐ ๐ต๐ถ 2 ฬ ฬ ฬ ฬ ฬ ฬ ๐ท๐ธ 2 ๐ต๐ถ ๐ท๐ธDE is a midsegment of ABC. Find the value of x.Ex.1Ex.2Ex.3Ex.4Ex.5 Solve for x.Ex.6 Solve for x.ฬ ฬ ฬ ฬ ฬ 12Ex.7 ๐บ๐ปWhat is the perimeter of GHJ?What is the perimeter of KLM?What is the relationship between theperimeter of GHJ and the perimeter of KLM?
GSE GeometrySimilarityNotesRight Triangle Similarity Theorem- If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed aresimilar to the original triangle and to each other.- Geometric Mean (Altitude) Theorem -In a right triangle, the altitude from the right angle to thehypotenuse divides the hypotenuse into two segments. The length of the altitude is thegeometric mean of the lengths of the two segments of the hypotenuse. ๐ถ๐ต๐ท ๐ด๐ต๐ถ ๐ด๐ถ๐ท ๐ด๐ต๐ถand ๐ถ๐ต๐ท ๐ด๐ถ๐ท๐ถ๐ท2 ๐ด๐ท ๐ต๐ทEx.1Ex.2Ex.4Ex.4
SSS Postulate: If all three sides of one triangle are proportional to corresponding sides of another triangle, then the triangles are similar. You can mark vertical angles and shared angles congruent! Explain why the triangles are similar (SSS , SAS , or AA ) and write a
Similar Triangles Solve Problems Using Properties of Similar Triangles Prove Similar Triangles ยท Use Definitions, Postulates, Theorems to Prove Triangles are Similar ยท Use Algebraic and Coordinates Methods to Prove Triangles are Similar Prove Triangles are Similar Using Deductive Proofs G.8 Right Triangles Pythagorean Theorem
Feb 14, 2011ย ยท Ch 4: Congruent Triangles 4โ1 Congruent Figures 4โ2 Triangle Congruence by SSS and SAS 4โ3 Triangle Congruence by ASA and AAS 4โ4 Using Congruent Triangles: CPCTC 4โ5 Isosceles and Equilateral Triangles 4โ6 Congruence in Right Triangles 4โ7 Using Corresponding Parts of Congruent Triangles
Congruent Triangles Strand: Triangles Topic: Exploring congruent triangles, using constructions, proofs, and coordinate methods Primary SOL: G.6 The student, given information in the form of a figure or statement will prove two triangles are congruent. Related SOL: G.4, G.5 Materials Congruent Triangles: Shortcuts activity sheet (attached)
a) Name the similar triangles. b) Write an extended proportion that is true for these triangles. c) If t 2, a 3, and n 6, find e. 6. Consider the triangles shown below. G R E T A a) Name the similar triangles. b) Write an extended proportion that is true for these triangles. c) If g 30, AT 36, and t 45, find GR. 7. Name the similar .
Unit 4: Congruent Triangles Unit Outcomes: In this unit, the students will classify triangles, find measures of angles in triangles, identify congruent figures, and prove triangles congruent. They will also use theorems about isosceles and equilateral triangles. Students will use coordinate geometry to investigate triangle relationships.
Unit 2: Triangles and Quadrilaterals Lesson 2.2 Use Isosceles and Equilateral Triangles Lesson 4.7 from Textbook Objectives Use properties of isosceles and equilateral triangles to find the measure of given angles. Use the Base Angles Theorem and Converse of the Base Angles Theorem to prove that parts of triangles are congruent.
KUTA Software: Angles & Triangles 10/18 45 4.2 Apply Congruence and Triangles pp 215 โ 221 (cont.) 10/21 PLAN TESTING (TBD) 7 [G-CO7] 46 4.4 Prove Triangles Congruent by SSS pp 232 - 237 8, 10 [G-CO8] [G-CO10] KUTA Software: Proving Triangles Congruent 10/22 47/48 4.5 Prove
Congruent Triangles Identify corresponding parts of congruent figures and be able to prove triangles congruent using SSS, ASA, SAS, AAS, and HL. Use congruent triangles to prove that the corresponding parts are congruent. Apply theorems about isosceles triangles and use the definition and theorems in proofs.
