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Class 10 - Mathematics, Term 1 - Triangles - 01, , 1. The line segments joining the midpoints of the adjacent sides of a quadrilateral form, a. arhombus, b. asquare, c. aparallelogram, d. arectangle, 2. In the equilateral triangle ABC if AD BC, then AD? is equal to, a 3CD?, b. 2C-D?, c 4CD?, a. CD?, 3. Ina A ABC, point D is on side AB and point E is on side AC, such that BCED is a trapezium. If DE : BC =, 3:5, then Area (A ADE): Area ( ABCED) =, a. 9:25, b. 3:5, ce 3:4, d. 9:16, 4. In the given figure, AP is equal to, A 4 B, , ‘er, , D 6 c, a. 7cm, , b. 6cm, , c S5cm, , d. 5.5cm, , PR, 5. Itis given that AABC ~ APQR, with =RS), , ar(BCA), , BC, QR, , , , = 5. Then is equal to, , a., , © we W olK, , b., &, d.
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7. In the given figure, BAC = 90° and AD | BC. Then,, A, , B D Cc, , a BC -CD= BC?, , b. BD- CD = AD?, , c AB- AC = BC?, , da. AB- AC = AD?, , 8. Itis given that AABC ~ ADFE. If ZA = 30°, ZC = 50°, AB = 5 cm, AC = 8 cm and DF = 7.5 cm then, , which of the following is true?, , a. DE=12 cm, ZF = 50°, , b. EF =12 cm, ZF= 10°, , c. EF=12cm, ZD = 100°, , d. DE=12cm, ZF = 100°, , ar(AABC) ., , 9. If AABC ~ APQR such that AB = 1.2 cm, PQ = 1.4 cm, then T(APOR) is, , a., b., a, a 9, , 10. What will be the length of the hypotenuse of an isosceles right triangle whose one side is 4\/2 cm, a. 12/2 em., b. 12cm., c 8cm., d. 8/2 em., , | enlomles, jos|enton!
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12., , 13., , 14,, , 15., , Assertion (A): In the AABC, AB = 24 cm, BC = 7 cm and AC = 25 cm, then A ABC is a right angle triangle., Reason (R): The ratio of the areas of two similar triangles is equal to the square of the ratio of their, corresponding sides., , Assertion: In A\ABC, DE | | BC such that AD = (7x - 4) cm, AE = (5x - 2) cm, DB = (3x + 4) cm, , and EC = 3x cm than x equal to 5., , Reason: If a line is drawn parallel to one side of a triangle to intersect the other two sides in distant point,, than the other two sides are divided in the same ratio., , Assertion (A): If areas of two triangles are 25 cm” and 64 cm’, the ratio of their corresponding medians or, angle bisectors or altitudes or sides will be 5 : 8., , Reason (R): The ratio of area of two similar triangles is the same as the ratio of squares of their, corresponding medians or angle bisectors or altitudes., , Assertion (A): If two triangles are similar and have an equal area, then they are congruent., , Reason (R): Corresponding sides of two triangles are equal, then triangles are congruent.
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Answer questions 16-20 based on the following case study:, , SCALE FACTOR AND SIMILARITY SCALE FACTOR: A scale drawing of an object is the same shape as the object, but a different size. The scale of a drawing is a comparison of the length used on a drawing to the length it, represents. The scale is written as a ratio., , SIMILAR FIGURES: The ratio of two corresponding sides in similar figures is called the scale factor., , i length in image, corresponding length in object, | one shape can become another using Resizing then the, , Scale factor, , shapes are Similar, , Rotation or Turn, Reflection or Flip, , , , ‘ Translation or Slide, , , , Hence, two shapes are Similar when one can become the other after a resize, flip, slide, or turn., , 16. A model of a boat is made on a scale of 1:4. The model is 120cm long. The full size of the boat has a width of, 60cm. What is the width of the scale model?
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17. What will affect the similarity of any two polygons?, a. They are flipped horizontally, b. They are dilated by a scale factor, c. They are translated down, d. They are not the mirror image of one another, 18. If two similar triangles have a scale factor of a: b. Which statement regarding the two triangles is true?, a. The ratio of their perimeters is 3a: b, b. Their altitudes have a ratio a: b, c. Their medians have a ratio z b, , d. Their angle bisectors have a ratio a; b*, 19. The shadow of a stick 5m long is 2m. At the same time, the shadow of a tree 12.5m high is:, , , , a. 3m, , b. 3.5m, , c 4.5m, , d. 5m, , 20. Below you see a student's mathematical model of a farmhouse roof with measurements. The attic floor,, , ABCD in the model, is a square. The beams that support the roof are the edges of a rectangular prism,, EFGHKLMN. E is the middle of AT, F is the middle of BT, G is the middle of CT, and H is the middle of DT. All, the edges of the pyramid in the model have a length of 12 m., , , , What is the length of EF, where EF is one of the horizontal edges of the block?, a. 24m, b. 3m, c 6m, d. 10m
