AD and BC are equal perpendiculars to a line segment AB (see Fig). Show that CD bisects AB.
AD and BC are equal perpendiculars to a line segment AB (see Fig). Show that CD bisects AB.
Solution and Explanation
In ∆BOC and ∆AOD,
∠BOC = ∠AOD (Vertically opposite angles)
∠CBO = ∠DAO (Each 90º)
BC = AD (Given)
∴ ∆BOC ≅∆AOD (AAS congruence rule)
∴ BO = AO (By CPCT)
⇒ CD bisects AB.
Top Questions on Congruence of Triangles
- In a regular polygon, each interior angle is 120 more than each exterior angle. Find the number of diagonals of the polygon.
- CAT - 2023
- Quantitative Aptitude
- Congruence of Triangles
- In a right-angled triangle Δ ABC , the altitude AB is 5 cm , and the base BC is 12 cm . P and Q are two points on BC such that the areas of ΔABP, ΔABQ , and Δ ABC are in arithmetic progression. If the area of Δ ABC is 1.5 times the area of Δ ABP , the length of PQ , in cm , is
- CAT - 2023
- Quantitative Aptitude
- Congruence of Triangles
- The minor angle between hours hand and minutes hand of a clock was observed at 8:48 am. The minimum deviation (in min) after 8:48 am on when angle increased by 50% is?
- CAT - 2023
- Quantitative Aptitude
- Congruence of Triangles
- In a right-angled triangle Δ ABC , the altitude AB is 5 cm , and the base BC is 12 cm . P and Q are two points on BC such that the areas of ΔABP, ΔABQ , and Δ ABC are in arithmetic progression. If the area of Δ ABC is 1.5 times the area of Δ ABP , the length of PQ , in cm , is
- CAT - 2023
- Quantitative Aptitude
- Congruence of Triangles
- Suppose the medians BD and CE of a triangle ABC intersect at a point O. If area of triangle ABC is 108 sq. cm, then, the area of the triangle EOD, in sq. cm, is
- CAT - 2022
- Quantitative Aptitude
- Congruence of Triangles
Questions Asked in CBSE Class IX exam
- Fig shows the distance-time graph of three objects A, B and C. Study the graph and answer the following questions:
- Which of the three is travelling the fastest?
- Are all three ever at the same point on the road?
- How far has C travelled when B passes A?
- How far has B travelled by the time it passes C?
- CBSE Class IX
- Graphical Representation of Motion
- Factorise : (i) x3 – 2x 2 – x + 2 (ii) x 3 – 3x 2 – 9x – 5 (iii) x 3 + 13x 2 + 32x + 20 (iv) 2y 3 + y 2 – 2y – 1.
- CBSE Class IX
- Factorisation of Polynomials
Use these adverbs to fill in the blanks in the sentences below.
awfully sorrowfully completely loftily carefully differently quickly nonchalantly(i) The report must be read ________ so that performance can be improved.
(ii) At the interview, Sameer answered our questions _________, shrugging his shoulders.
(iii) We all behave _________ when we are tired or hungry.
(iv) The teacher shook her head ________ when Ravi lied to her.
(v) I ________ forgot about it.
(vi) When I complimented Revathi on her success, she just smiled ________ and turned away.
(vii) The President of the Company is ________ busy and will not be able to meet you.
(viii) I finished my work ________ so that I could go out to play
- CBSE Class IX
- The fun they had
- What are the main features of the mechanical teachers and the schoolrooms that Margie and Tommy have in the story?
- CBSE Class IX
- The fun they had
- A driver of a car travelling at \(52\) \(km \;h^{–1}\) applies the brakes Shade the area on the graph that represents the distance travelled by the car during the period. (b) Which part of the graph represents uniform motion of the car?
- CBSE Class IX
- Graphical Representation of Motion