This document contains 11 math problems related to triangles and their properties. The problems cover topics like defining different types of triangles based on their angles (e.g. equilateral, right, obtuse), finding missing angles and sides of triangles using properties like angle sum is 180 degrees, using trigonometry to calculate lengths of ladder placed against a wall, proving relationships between sides and angles of triangles, and finding unknown angles or sides given information about ratios of angles or consecutive integers representing angles. The document provides practice for students on key concepts in triangles.

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St. Joseph’s International School, Hisar
Class: VII Name:____________________ Roll No. ___
Subject: Mathematics Chapter: Triangle and its properties
1. Fill inthe banks:
(i) Triangle isformedbyjoiningthree ______________ points.
(ii) A pointwhere twosidesof atriangle meetisknownas______________ of a triangle.
(iii) Eachangle of an equilateraltriangle isof ______________ measure.
(iv) A ______________ triangle hasone angle of 90°.
(v) A triangle has______________ verticesand______________ sides.
(vi) Inan obtuse triangle,the remainingtwoanglesare ______________
(vii) The sumof the measure of three anglesof a triangle is______________
(viii) A triangle whose twosidesare of equal lengthisknownas______________ triangle.
2. ABCD isa quadrilateral.Showthat:AB+ BC + CD + DA > AC+ BD .
3. (i) A ladderisplacedalonga wall at a distance of 5 m from it.The laddertouchesa window inthe wall ata heightof
12 m. Findthe lengthof the ladder.
(ii) A ladderof length13m isplacedalonga wall at a heightof 12m. Findthe distance of footof ladderfromwall.
4. In the above figure,Pisa pointon the side BC of ∆ ABC.Prove that
AB + BC + AC > 2AP
5. In the above figure,the school andlibraryroadsmeetat an angle of 90°, findthe distance betweenNelsonMiddle
School and Library.
6. Referto∆ABC and name the following.
(i) a medianof ∆ABC ________

2. (ii) an altitude of ∆ABC________
(iii) a bisectorof an angle of ∆ABC___________
7. In a triangle,if the secondangle is5° greaterthanthe firstangle andthe thirdangle is5° greaterthan secondangle,
findthe three anglesof the triangle.
8. In a triangle,if the secondangle is2 timesthe firstangle andthe thirdangle is3 timesthe firstangle,findthe angles
of the triangle.
9. If the anglesof a triangle are inthe ratio 2 : 7 : 11, thenfindthe angles.
10. If 3 consecutive positiveintegersbe the anglesof atriangle,thenfindthe three anglesof the triangle.
11. In a triangle,if the secondangle is2 timesthe firstangle andthe thirdangle is3 timesthe firstangle,findthe angles
of the triangle.
12. Findthe value of unknowns.