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Chapter 3: Q25 (page 98)

Given: ∠ABD≅∠AED

Prove: ∠C≅∠F

Short Answer

Expert verified

It is proved that ∠C≅∠F.

Step by step solution

01

Step 1. Observe the figure and highlight angle C and angle F .

02

Step 2. Apply the definition of vertically opposite angles.

Vertically opposite angles are the opposite angles formed due to intersection of two lines.

Consider ΔBDCandΔEDF,

∠BDCand∠EDFare vertically opposite angles, therefore, ∠BDC=∠EDF.

Also, ∠DBC=∠DEF.

03

Step 3. Apply corollary 1.

If two angles of one triangle are congruent to two angles of another triangle then third angles are congruent.

Therefore, ∠C≅∠F.

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