Construct a ∆ X Y Z in which ∠ Y = 45 0 , ∠ Z = 75 0 and X Y + Y Z + Z X = 12 c m .

Given: ∠ Y = 45 0 , ∠ Z = 75 0 X Y + Y Z + Z X = 12 c m (i) Draw a line segment P Q = 12 c m (ii) Draw a ray make an angle 45 0 at P and draw another ray make an angle 75 0 at Q. (iii) Bisect both angles such that bisector of angles intersect at point X . (iv) Draw a perpendicular bisector of P X and Q X . (v) both bisectors intersect line P Q on point Y and Z (vi) Meet point X to Y and X to Z . Thus Δ X Y Z is required triangle.

Construct △ P Q R , in which ∠ Q = 60 ° , ∠ R = 80 ° and P Q + Q R + R S = 11 cm .

Given: ∠ Q = 70 ° , ∠ R = 80 ° and perimeter of △ P Q R = 11 cm . Steps of construction: I . Draw a line segment A B of 11 cm . I I . From point A draw a ray A D at 60 ° and from B draw a ray B E at 80 ° . I I I . Draw an angle bisector of A and B , two angle bisectors intersect each other at point L . I V . Draw a line bisector of A P and B P respectively these two-line bisectors intersect at point Q and R . V . Join P Q and P R . △ P Q R is required triangle.

HARD

Earn 100

Prove that two triangles having the same base and equal areas lie between the same parallels.

Important Questions on Areas of Parallelograms and Triangles

HARD

Mathematics>Geometry>Areas of Parallelograms and Triangles>Figures on Same Base and between the Same Parallels

Construct a

∆ X Y Z

in which

\Rightarrow \frac{1}{2} \times A B \times C E = \frac{1}{2} \times D F \times A B

and

X Y + Y Z + Z X = 12 c m

MEDIUM

Mathematics>Geometry>Areas of Parallelograms and Triangles>Figures on Same Base and between the Same Parallels

Construct $△ P Q R$ , in which $C D F E$ and $P Q + Q R + R S = 11 cm$ .

MEDIUM

Mathematics>Geometry>Areas of Parallelograms and Triangles>Figures on Same Base and between the Same Parallels

Construct $△ X Y Z$ in which $∠ Y = 58 °, ∠ X = 46 °$ and perimeter of triangle is $10.5 cm$ .

EASY

Mathematics>Geometry>Areas of Parallelograms and Triangles>Figures on Same Base and between the Same Parallels

Let $ABC$ be a triangle in which $BC = 5 cm, ∠ B = 60 °$ and $AC + AB = 7 .5 cm .$ Given below are the steps of constructing the $△ ABC .$ Which of the following steps is INCORRECT?
Step I: Draw a line segment $BC$ of length $5 cm .$
Step II: Draw an $∠ XBC = 60 °$ at point $B$ of line segment $BC .$
Step III: Cut off $PB = 3 .5 cm$ on the ray $BX .$
Step IV: Join $PC .$ .
Step V: Draw $⊥$ bisector of $BC$ which intersect ray $BX$ at $A .$ Join $AC .$
Step VI: $△ ABC$ is the required triangle.