Title Class 9 Mathematics Chapter 7 Triangles.pdf ✅

Triangles DPP-01 [Topic: Side-Angle-Side Congruence Criterion] Very Short Answer Type Questions 1. In △ AAAAAA and △ DEF, AAAA = DDDD and ∠A = ∠D. By SAS axiom, which one condition is necessary to show that △ ABC ≅△ DEF ? 2. To show △ AAAAAA ≅△ PPPPPP by SS SS axiom, when AAAA = PPPP = 3cm and = = 4cm, then write other necessary condition. 3. In triangles AAAAAA and PPPPPP, AAAA = PPPP and ∠ = ∠ , which condition is required for △ AAAAAA ≅△ PPPPPP by SS SS axiom? 4. In △ PPPPPP, if PPPP = PPPP and ∠ = 65∘ , then find ∠ . 5. In △ AAAAAA, if AAAA = AAAA, ∠ = 50∘ , then find ∠AA. 6. In the given figure, if AAAA = AAAA, then what is the value of xx ? Short Answer Type Questions-I 7. AB is a line segment and line ll is its perpendicular bisector. If a point PP lies on ll, show that PP is equidistant from AA and . 8. Show that measure of each angle of an equilateral triangle is 60∘ . 9. In △ AAAAAA, AA is the perpendicular bisector of . Show that △ AAAAAA is an isosceles triangle in which AB = AC. 10. In the given figure, AB = AC,DB = DC. Prove that ∠ABD = ∠ACD. Short Answer Type Questions-II
11. In the figure given below, ABC is a triangle in which AB = AC. X and Y are points on AB and AC such that AAAA = AAAA. Prove that △ BCX ≅△ CBY. 12. In the given figure, AB = CF, EF = BD, ∠AFE = ∠CBD. Prove that (i) △ AFE ≅△ CBD (ii) ∠D = ∠E 13. In the given figure, AAAAAA is an isosceles triangle in which AAAA = AAAA and LLLL is parallel to . If ∠A = 50∘ , find ∠LMC. 14. In the figure, it is given that AAAA = AA and = . Prove that △ AAAAAA ≅△ AA AA. 15. In quadrilateral AAAAAA , AAAA = AA and AAAA bisects ∠A. Show that △ AAAAAA ≅△ AAAA . What can you say about BC and BD ?
16. In the given figure, ∠EAB = ∠EBA and AC = BD. Prove that AD = BC. Long Answer Type Questions 17. In an isosceles △ ABC with AB = AC,D and E are two points on BC such that BE = CD. Show that △ ADE is an isosceles triangle. 18. Prove that △ AAAAAA is isosceles if any one of the following holds: (i) altitude AD bisects BC (ii) median AD is perpendicular to the base BC. 19. ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA. Prove that: (i) △ ABD ≅△ BAC