![]() If the premise is true, then the converse could be true or false: If the original conditional statement is false, then the converse will also be false. ![]() Now it makes sense, but is it true? Not every converse statement of a conditional statement is true. Converse Of the Isosceles Triangle Theorem The Converse of the Isosceles Triangle Theorem states: If two angles of a triangle are congruent, then sides opposite those angles are congruent. So here once again is the Isosceles Triangle Theorem: You may need to tinker with it to ensure it makes sense. The converse of a conditional statement is made by swapping the hypothesis (if …) with the conclusion (then …). So if the two triangles are congruent, then corresponding parts of congruent triangles are congruent (CPCTC), which means:Ĭonverse of the isosceles triangle theorem We just showed that the three sides of △DUC are congruent to △DCK, which means you have the Side Side Side Postulate, which gives congruence. There! That's just DUCK! Look at the two triangles formed by the median. We find Point C on base UK and construct line segment DC: Isosceles Triangle Theorem Example To mathematically prove this, we need to introduce a median line, a line constructed from an interior angle to the midpoint of the opposite side. ![]() The Isosceles Triangle Theorem states: If two sides of a triangle are congruent, then angles opposite those sides are congruent. Knowing the triangle's parts, here is the challenge: how do we prove that the base angles are congruent? That is the heart of the Isosceles Triangle Theorem, which is built as a conditional (if, then) statement: The two angles formed between base and legs, ∠DUK and ∠DKU, or ∠D and ∠K for short, are called base angles. The third side is called the base (even when the triangle is not sitting on that side). ∠DU ≅ ∠DK, so we refer to those twins as legs. Like any triangle, △DUK has three sides: DU, UK, and DK Like any triangle, △DUK has three interior angles: ∠D, ∠U, and ∠K What else have you got? Properties of an isosceles triangle If these two sides, called legs, are equal, then this is an isosceles triangle. Hash marks show sides ∠DU ≅ ∠DK, which is your tip-off that you have an isosceles triangle. You can draw one yourself, using △DUK as a model. Get the free view of Chapter 10, Isosceles Triangles Concise Mathematics Class 9 ICSE additional questions for Mathematics Concise Mathematics Class 9 ICSE CISCE,Īnd you can use to keep it handy for your exam preparation.Here we have on display the majestic isosceles triangle, △DUK. Maximum CISCE Concise Mathematics Class 9 ICSE students prefer Selina Textbook Solutions to score more in exams. ![]() The questions involved in Selina Solutions are essential questions that can be asked in the final exam. Using Selina Concise Mathematics Class 9 ICSE solutions Isosceles Triangles exercise by students is an easy way to prepare for the exams, as they involve solutionsĪrranged chapter-wise and also page-wise. Selina textbook solutions can be a core help for self-study and provide excellent self-help guidance for students.Ĭoncepts covered in Concise Mathematics Class 9 ICSE chapter 10 Isosceles Triangles are Isosceles Triangles, Isosceles Triangles Theorem, Converse of Isosceles Triangle Theorem. This will clear students' doubts about questions and improve their application skills while preparing for board exams.įurther, we at provide such solutions so students can prepare for written exams. Selina solutions for Mathematics Concise Mathematics Class 9 ICSE CISCE 10 (Isosceles Triangles) include all questions with answers and detailed explanations. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. has the CISCE Mathematics Concise Mathematics Class 9 ICSE CISCE solutions in a manner that help students Chapter 1: Rational and Irrational Numbers Chapter 2: Compound Interest (Without using formula) Chapter 3: Compound Interest (Using Formula) Chapter 4: Expansions (Including Substitution) Chapter 5: Factorisation Chapter 6: Simultaneous (Linear) Equations (Including Problems) Chapter 7: Indices (Exponents) Chapter 8: Logarithms Chapter 9: Triangles Chapter 10: Isosceles Triangles Chapter 11: Inequalities Chapter 12: Mid-point and Its Converse Chapter 13: Pythagoras Theorem Chapter 14: Rectilinear Figures Chapter 15: Construction of Polygons (Using ruler and compass only) Chapter 16: Area Theorems Chapter 17: Circle Chapter 18: Statistics Chapter 19: Mean and Median (For Ungrouped Data Only) Chapter 20: Area and Perimeter of Plane Figures Chapter 21: Solids Chapter 22: Trigonometrical Ratios Chapter 23: Trigonometrical Ratios of Standard Angles Chapter 24: Solution of Right Triangles Chapter 25: Complementary Angles Chapter 26: Co-ordinate Geometry Chapter 27: Graphical Solution (Solution of Simultaneous Linear Equations, Graphically) Chapter 28: Distance Formula ![]()
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