Genius Jnr - In Fig., P is the point on the side BC. Complete each of the following statements using symbol ' = ', '>' or '<' so as to make it true: (i) AP ... AB + BP (ii) AP .... AC + PC (iii) AP....12(AB+AC+BC)

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In Fig., P is the point on the side BC. Complete each of the following statements using symbol ' = ', '>' or '<' so as to make it true:

(i) AP ... AB + BP
(ii) AP .... AC + PC
(iii)

A P . . . . \frac{1}{2} (A B + A C + B C)

or

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Difference Triangle Triangular Region Fig B C Four Points Three Points Collinear Ac Bd Intersect Eight Triangles Observe Name Triangles Fig Point Side Bc Abc Ad Joined Name Triangles Observe Figure Many Distinguish Triangle Triangular Region Take Three Collinear Points B C Page Note Book Join Ab Bc Ca Figure Triangle Take Three Non Collinear Points B C Page Notebook Join Ab Bc Ca Figure Get Name Triangle Also Name S Angles Triangle X 40 X 20 12x 10 Find Value X Angles Triangle Ratio 1 2 3 Determine Three Angles Three Angles Triangle Equal One Another Measure Angles One Angles Triangle 130 Two Angles Equal Measure Equal Angles Two Angles Triangle Measures 105 30 Find Measure Third Angle Following State Statement True False F Triangle Three Sides Ii Triangle May Four Vertices Iii Three Fill Blanks Correct Word Symbol Make True Statement Triangle Sides Ii Triangle Vertices Iii Triangle Fig Five Triangles Measures Angles Indicated State Triangle Whether Acute Right Obtuse Fig Length Cm Side Indicated Along Side State Triangle Whether Scalene Isosceles Equilateral Explain Following Terms Triangle Ii Parts Elements Triangle Iii Scalene Triangle Iv Isosceles Triang Find X Z Whichever Required Figures Given Six Cornered Figure Ac Ad Ae Joined Find Fab Abc Bcd Cde Def Efa One Angle Triangle Greater Sum Two Say Measure Angle Type Triangle Two Acute Angles Right Triangle Equal Find Two Angles Angles Triangle Ratio 3 4 5 Find Smallest Angle Following Measures Three Angles Given State Cases Angles Possibly Triangle 63 37 80 Ii 45 61 73 Iii Angle Triangle Less Sum Two Show Triangle Acute Angled One Angle Triangle Equal Sum Two Show Triangle Right Triangle Two Angles Triangle Equal Third Angle Greater Angles 30 Determine Angles Triangle Angles Triangle Arranged Ascending Order Magnitude Difference Two Consecutive Angles 10 Find Three A Abc B 60 C 40 Al Bc Ad Bisects L Lie Side Bc Find Lad Abc 50 Bc Produced Point Bisectors Abc Acd Meet E Find E Bisectors Acute Angles Right Triangle Meet Find Angle Two Bisectors Abc 60 B 80 Bisectors B C Meet Find C Ii Boc Abc 50 B 70 Bisector C Meets Ab Find Angles Triangles Adc Bdc Abc 100 Ad Bisects Ad Bc Find B Possible Triangle Two Angles Right Ii Two Angles Obtuse Iii Two Angles Acute Iv Angle Less 60 V Angl Abc 3 4 B 6 C Calculate Angles One Angle Triangle 100 Two Angles Ratio 2 3 Find Angles One Angle Triangle 60 Two Angles Ratio 1 2 Find Angles Student Asked Measure Two Exterior Angles Abc Observed Exterior Angles B 103 74 Respectively Possibl Fig Ac Ce B C 3 2 1 Find Value Ecd Fig Sides Bc Ca Ba Abc Produced E F Respectively Acd 105 Eaf 45 Find Angles Abc Exterior Angles Obtained Producing Base Triangle Ways 104 136 Find Angles Triangle One Exterior Angles Triangle 80 Interior Opposite Angles Equal Measure Two Angles Triangle Exterior Angle Vertex 95 One Interior Opposite Angles 55 Find Angles Triangle Fig Two Angles Indicated Measures Acx Acb Fig Cbx Exterior Angle Abc B Name Interior Adjacent Angle Ii Interior Opposite Angles Exterior Cbx A Fig Abc Right Angled Q R Points Line Bc P Point Qp Ac Rp Ab Find P Line Segments Ab Cd Intersect Ac Db Cab 35 Cdb 55 Find Bod Fig P Point Side Bc Complete Following Statements Using Symbol Make True Ap Ab Bp Ii Ap Ac Pc Iii Ap Following Three Positive Numbers State Numbers Could Possibly Lengths Sides Triangle 5 7 9 Ii 2 10 1 Compute Value X Following Figures Explain Concept Interior Exterior Angles Figures Given Find X Point Side Bc Abc Line Pdq Meets Side Ac P Ab Produced Q 80 Abc 60 Pdc 15 Find Aqd Ii Apd Side Bc Abc Produced Point Bisector Meets Side Bc L Abc 30 Acd 115 Find Alc Abc Triangle B C Ray Ax Bisects Exterior Angle Dac Dax 70 Find Acb Fig Abc Right Triangle Right Angled Lies Ba Produced De Bc Intersecting Ac F Afe 130 Find Bde Ii Bca Fig Measures Angles Indicated Find Value X Fig Ad Cf Respectively Perpendiculars Sides Bc Ab Abc Fcd 50 Find Bad Two Poles Heights 6 11 Stand Plane Ground Distance Feet 12 Find Distance Tops Hint Find Hypotenuse R Sides Certain Triangles Given Determine Right Triangles 7 Cm B 24 Cm C 25 Cm Ii 9 Cm B 16 Cm C 18 Cm Sides Triangle 3 Cm 4 Cm 6 Cm Long Determine Whether Triangle Right Angled Triangle Ladder 3 7 Long Placed Wall Way Foot Ladder 1 2 Away Wall Find Height Wall Ladder Reaches Hypotenuse Triangle 2 5 Cm One Sides 1 5 Cm Find Length Side Right Abc Lengths Legs Given Find Length Hypotenuse 6 Cm B 8 Cm Ii 8 Cm B 15 Cm Iii 3 Cm B 4 Cm Iv 2 State Pythagoras Theorem Converse Abc 100 B 30 C 50 Name Smallest Largest Sides Triangle Point Exterior Abc Symbol Use Complete Statement Oa Ob Ab Write Two Similar Statements Shown Oa Ob O P Point Interior Abc Shown Fig State Following Statements True False F Ap Pb Ab Ii Ap Pc Ac Iii Bp P Draw Triangle Abc Ac 4 Cm Bc 3 Cm C 80 Measure Ab Ab 2 Ac 2 Bc 2 One Following True Ab 2 Ac 2 Bc 2 A Draw Triangle Abc Ac 4 Cm Bc 3 Cm C 105 Measure Ab Ab 2 Ac 2 Bc 2 One Following True Ab 2 Ac 2 Bc 2 Abc Ad Altitude Ad 12 Cm Bd 9 Cm Dc 16 Cm Examine Abc Right Angled Abc Abc 100 Bac 35 Bd Ac Meets Side Ac Bd 2 Cm Find C Length Dc Verify Following Numbers Represent Pythagorean Triplet 12 35 37 Ii 7 24 25 Iii 27 36 45 Iv 15 36 39 Two Legs Right Triangle Equal Square Hypotenuse 50 Find Length Leg Ladder 50 Dm Long Set Wall House Reaches Window Height 48 Dm Far Lower End Ladder Base Wall Foot Ladder 6 Away Wall Top Reaches Window 8 Ground Ladder Shifted Way Foot 8 Away Wall Height Top R Man Goes 15 Due West 8 Due North Far Starting Point Measures Angles Triangle 2x 3x 5 4x 13 Value X 22 B 18 C 20 30 Use Following Information Answer Next Question Rupam Performs Experiment Find Whether Burning Candle Abc 2 3 B 6 C Th Measure Smallest Angle 90 B 60 C 40 30 Abc B 150 B C 75 B 35 B 45 C 55 25 Abc B 33 B C 18 B 35 B 45 C 55 25 Measures Angles Triangle 2x 5 3x 12 30 X2 X 3119 B 3099 C 3109 3019 Fig 59 Value X 84 B 74 C 94 57 Fig 60 Values X X 20 130 C X 20 140 B X 40 140 X 15 140 Fig 61 Value Xis 72 B 50 C 58 48 Meena Mother Delivered Baby Boy Excited Wonders Eggs Get Converted Baby Boy Baby Girl Meena Approach Use Following Information Answer Next Question Mohan Mother Delivered Baby Girl Wants Know Teacher E Fig 64 Ab Cd Values X X 21 28 B X 21 38 C X 38 21 X 22 38 Fig 65 Ab Ce Values X X 26 144 B X 36 154 C X 154 36 X 144 26 Fig 66 Af De X 37 B 57 C 47 67 Fig 67 Values X X 130 120 B X 120 130 C X 120 120 X 130 130 Fig 68 Values X X 120 150 B X 110 160 C X 150 120 X 110 160 Fig 69 Ab Cd Values X X 106 307 B X 307 106 C X 107 306 X 105 308 Fig 70 Ab Cd Values X X 24 48 B X 34 68 C X 24 68 X 34 48 Fig 71 Ab Cd Values X Z X 56 47 Z 77 B X 47 56 Z 77 C X 77 56 Z 47 X 56 77 Z 47 Exterior Angles Triangle 2x 10 3x 5 2x 40 X 25 B 35 C 45 55 Fig 73 Value X 20 B 30 C 40 25 Fig 74 Ab Co Cab 49 Cbd 27 Bdc 112 Values X X 41 90 B X 41 63 C X 63 41 X 90 41 Following Set Measures Sides Triangle 8 Cm 4 Cm 20 Cm B 9 Cm 17 Cm 25 Cm C 11 Cm 16 Cm 28 Cm None Following Cases Right Triangle Cannot Constructed 12 Cm 5 Cm 13 Cm B 8 Cm 6 Cm 10 Cm C 5 Cm 9 Cm 11 Following Pythagorean Triplet 3 4 5 B 8 15 17 C 7 24 25 13 26 29 Right Triangle One Acute Angles Four Times Measure 68 B 84 C 80 72 Following Cases Right Triangle Abc Constructed Ab 5 Cm Bc 7 Cm Ac 10 Cm B Ab 7 Cm Bc 8 Cm Ac 12 Cm C Abc Right Triangle Right Angled Ab 24 Cm Ac 7 Cm Bc 31 Cm B 17 Cm C 25 Cm 28 Cm Abc Isosceles Right Triangle Right Angled C Ac 5 Cm Ab 2 5cm B 52 Cm C 10 Cm 5 Cm Use Following Information Answer Next Question Himesh Rubbed Pencil Tip Rubber Sheet Glass Surface W Ladder Placed Way Foot 15 Away Wall Top Reaches Window 20 Ground Length Ladder 35 B 25 C 18 17 5 Hypotenuse Right Triangle 26 Cm Long One Remaining Two Sides 10 Cm Long Length Side 25 Cm B 23 Cm C 15 Long Ladder Placed Wall Away Foot Ladder 9 Away Wall Height Ladder Reach Wall 13 B 10 C 8 12 Fig 72 Ab Cd Ae Bd Value X 38 B 48 C 58 68