Q6 of 70 Page 140

Fill in the blanks so that the following statements are true:

and are the altitudes of ΔABC. If AB = 12, AC = 9.9, AD = 8.1 and BE = 7.2, perimeter of ΔABC = _____.

We have



Given that: AD and BE are altitudes of ∆ABC. ⇒ ∠ADC = ∠


In ∆ADC and ∆BEC,


∠ADC = ∠BEC [∵, ∠ADC = ∠BEC = 90° as AD and BE ]


∠ACD = ∠BCE [∵, ∠ACD and ∠BCE are same angles of the same triangles, so they obviously are equal]


⇒ By AA-corollary, we can say that ∆ADC ∼ ∆BEC for the correspondence of ADC ↔ BEC.


By definition, for a given correspondence between the vertices of two triangles, if the corresponding angles of the triangles are congruent and the lengths of the corresponding sides are in proportion, then the given correspondence is a similarity between two triangles.


⇒


⇒


⇒


⇒ BC = 8.8


So, perimeter of ∆ABC is given by


Perimeter of ∆ABC = AB + BC + AC


⇒ Perimeter of ∆ABC = 12 + 8.8 + 9.9


⇒ Perimeter of ∆ABC = 30.7


Thus, perimeter of ∆ABC = 30.7.


More from this chapter

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4

The correspondence ABC ↔ DEF is similarity in ΔABC and ΔDEF. is an altitude of ΔABC and is an altitude of ΔDEF. Prove that AB X DN = AM X DE.

 5

Explain with reasons, whether the following statements are true or false:

(1) AAA criterion of similarity of triangles cannot be the criterion for congruence of triangles.


(2) SAS criterion for congruence of triangles cannot be a criterion for similarity of triangles.


(3) Two congruent triangles have the same area.


(4) Two similar triangles always have the same area.


(5) Area of similar triangles are proportional to the squares of measures of their corresponding angles.

 6

Fill in the blanks so that the following statements are true:

D, E, F are respectively the mid-points of , , of ΔPQR. The correspondence DEF ↔ _____ is similarity.

 6

Fill in the blanks so that the following statements are true:

In ΔABC, and are altitudes. If AB = 12, BC = 15 and AM = 9.6, then CN = _____.