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# Geometry

## PDF| Exercise 10.1|Class 7(seven)|Congruence

Exercise – 10.1-class seven

## Exercise 10.1|Class seven| Congruence| Part – 2

Problem – 5: In the figure, AD = AE, BD = CE and ∠AEC = ∠ADB. Prove that AB = AC. Particular enunciation: In the figure, AD = AE, BD = CE and ∠AEC = ∠ADB. We have to prove that AB = AC. Proof: In ∆ACE and ∆ADB, AD ...

## Solution exercise 9.1| Class seven| Geometry

Problem-1: In the figure, ∆ABC is a triangle in which ∠ABC = 900, ∠BAC =480 and BD is perpendicular to AC. Find the remaining angles. Solution: Let remaining angles ∠ABD = x, ∠DBC = y and ∠BCD = z. Since BD⊥AC ∴ ∠ADB = ∠CDB = 900 Now, in ∆ABD ...

## Exercise 10.1|Class seven| Congruence| Part – 1

Problem – 1: In the figure, CD is the perpendicular bisector of AB, Prove that ∆ADC ≅ ∆BDC. Solution: Particular enunciation: Given that, in the figure, CD is the perpendicular bisector of AB. i.e., AD = BD. We have to prove that, ∆ADC ≅ ∆BDC. Proof: In ∆ADC and ∆BDC, ...

## If two triangles have the three sides of the one equal to the three sides of the other, each to each, then they are equal in all respects.

If two triangles have the three sides of the one equal to the three sides of the other, each to each, then they are equal in all respects.   Particular enunciation: In the ∆ABC and ∆DEF, AB = DE, AC = DF and BC = EF, We have to proved ...

## If two angles of triangles are equal, then the sides opposite to the equal angles are equal.

If two angles of triangles are equal, then the sides opposite to the equal angles are equal. Particular enunciation: Let ABC be a triangle in which the ∠ACB = the ∠ABC. We have to prove that AB =AC. Proof: If AC and AB are equal, suppose that AB>AC. From BA ...

## Solution of exercise 9.2(Triangle)| Class seven

Problem-9: In the triangle ABC, AB>AC and the bisectors of the ∠B and ∠C intersect at the point P. Prove that PB>PC. Particular enunciation: Given that, in the triangle ABC, AB>AC and the bisectors of the ∠B and ∠C intersect at the point P. We have to prove that PB>PC. ...

## If two sides of a triangle are equal, then the angles opposite the equal sides are also equal

General enunciation: If two triangles have two sides of the one equal to two sides of the other, each to each, the angles included by those sides are also equal then the triangles are equal in all respect. Particular Enunciation: Let, ∆ABC and ∆DEF be two triangles in which AB=DE, ...