Q144 of 158 Page 159

ABC is an isosceles triangle with AB = AC and D is the mid-point of base BC (Fig. 6.48).

A. State three pairs of equal parts in the triangles ABD and ACD.


B. Is ∆ABD ≅ ∆ACD. If so why?


Given: AB = AC; D is midpoint of BC


As D is midpoint of BC


BD = DC


In Δ ADB and Δ ADC


AB = AC (given)


BD = DC (D is midpoint of BC)


AD = AD (common)


⇒ these are all 3 equal parts of triangles ABD and ACD


⇒ yes ∆ABD ≅ ∆ACD


Because it follows SSS congruence criterion


More from this chapter

All 158 →
142

Without drawing the triangles write all six pairs of equal measures in each of the following pairs of congruent triangles.

(a) ∆STU ≅ ∆DEF


(b) ∆ABC ≅ ∆LMN


(c) ∆YZX ≅ ∆PQR


(d) ∆XYZ ≅ ∆MLN

 143

In the following pairs of triangles of Fig. 6.47, the lengths of the sides are indicated along the sides. By applying SSS congruence criterion, determine which triangles are congruent. If congruent, write the results in symbolic form.





 145

In Fig. 6.49, it is given that LM = ON and NL = MO

A. State the three pairs of equal parts in the triangles NOM and MLN.


B. Is ∆NOM ≅ ∆MLN. Give reason?


 146

Triangles DEF and LMN are both isosceles with DE = DF and LM = LN, respectively. If DE = LM and EF = MN, then, are the two triangles congruent? Which condition do you use?

If ∠E = 40°, what is the measure of ∠N?