If $∆DEF ≅ ∆BCA$, write the part(s) of $∆BCA$ that correspond to
$(i).\ \angle E$
$(ii).\ \overline{EF}$
$(iii).\ \angle F$
$(iv).\ \overline{DF}$
Given: $∆DEF ≅ ∆BCA$.
To do: To write the part(s) of $∆BCA$ that correspond to
$(i).\ \angle E$
$(ii).\ \overline{EF}$
$(iii).\ \angle F$
$(iv).\ \overline{DF}$
Solution:
Given that $∆ DEF ≅ ∆ BCA$
Since we know that corresponding parts of congruent triangles are equal, hence we can say that the corresponding sides and angles of both congruent triangles are equal.
$(i).\ ∠E=∠C$
$(ii)$. side $EF=$side $CA$
$(iii).\ ∠F=∠A$
$(iv).$ side $DF=$side $BA$
Related Articles
- Construct $∆DEF$ such that $DE = 5\ cm$, $DF = 3\ cm$ and $\angle EDF = 90^{\circ}$.
- $S$ and $T$ are points on sides $PR$ and $QR$ of $∆PQR$ such that $\angle P = \angle RTS$. Show that $∆RPQ \sim ∆RTS$.
- Examine whether you can construct $∆DEF$ such that $EF = 7.2\ cm$, $m\angle E = 110^{\circ}$ and $m\angle F = 80^{\circ}$. Justify your answer.
- D, E and F are respectively the mid-points of sides AB, BC and CA of $∆ABC$. Find the ratio of the areas of $∆DEF$ and $∆ABC$.
- In $∆ABC$, $\angle A=30^{\circ},\ \angle B=40^{\circ}$ and $\angle C=110^{\circ}$In $∆PQR$, $\angle P=30^{\circ},\ \angle Q=40^{\circ}$ and $\angle R=110^{\circ}$. A student says that $∆ABC ≅ ∆PQR$ by $AAA$ congruence criterion. Is he justified? Why or why not?
- Let $∆ABC \sim ∆DEF$ and their areas be respectively $64\ cm^2$ and $121\ cm^2$. If $EF = 15.4\ cm$, find BC.
- CD and GH are respectively the bisectors of $\angle ACB$ and $\angle EGF$ such that D and H lie on sides AB and FE of $∆ABC$ and $∆EFG$ respectively. If $∆ABC \sim ∆FEG$, show that (i) \( \frac{\mathrm{CD}}{\mathrm{GH}}=\frac{\mathrm{AC}}{\mathrm{FG}} \)>(ii) \( \triangle \mathrm{DCB} \sim \triangle \mathrm{HGE} \)>(iii) \( \triangle \mathrm{DCA} \sim \triangle \mathrm{HGF} \)
- ∆ABC ~ ∆LMN. In ∆ABC, AB = 5.5 cm, BC = 6 cm, CA = 4.5 cm. Construct ∆ABC and ∆LMN such that $\frac{BC}{MN} \ =\ \frac{5}{4}$.
- If $∆ABC ≅ ∆FED$ under the correspondence $ABC\Leftrightarrow FED$, write all the corresponding congruent parts of the triangles.
- $E$ is a point on the side $AD$ produced of a parallelogram $ABCD$ and $BE$ intersects $CD$ at $F$. Show that $∆ABE \sim ∆CFB$.
- Construct $∆ABC$, given $m\angle A = 60^{\circ}$, $m\angle B = 30^{\circ}$ and $AB = 5.8\ cm$.
- Construct $∆PQR$ if $PQ = 5\ cm$, $m\angle\ PQR = 105^{\circ}$ and $m\angle QRP = 40^{\circ}$. [Hint: Recall angle-sum property of a triangle.]
Kickstart Your Career
Get certified by completing the course
Get Started