In triangle ABC- AB - AC- BE perp AC and CF perp AB-State whether following statement is true or falseAF - AETrueFalse

Question

Toppr Admin · Accepted Answer

In -x25B3-BFC and -x25B3-BEC-BC-BC -Common-x2220-FCB-x2220-EBC -Given- AB - AC-x2220-BFC-x2220-BEC -each 90-x2218-Thus- -x25B3-BFC-x2245-x25B3-CEB -ASA rule-Hence- BF-CE -By cpct-AB-AC -Given-Hence- AB-x2212-BF-AC-x2212-CEAF-AE

In triangle ABC, $A B = A C$ ; $B E$ $⊥$ $A C$ and $C F$ $⊥$ $A B$ .
State whether following statement is true or false
$A F = A E$

True
False

In $△ B F C$ and $△ B E C$ ,
$B C = B C$ (Common)
$∠ F C B = ∠ E B C$ (Given, AB = AC)
$∠ B F C = ∠ B E C$ (each $90^{\circ}$ )
Thus, $△ B F C ≅ △ C E B$ (ASA rule)
Hence, $B F = C E$ (By cpct)
$A B = A C$ (Given)
Hence, $A B - B F = A C - C E$
$A F = A E$

In triangle ABC, AB=AC; BE ⊥ AC and CF ⊥ AB.State whether following statement is true or falseAF=AETrueFalse

In △BFC and △BEC,BC=BC (Common)∠FCB=∠EBC (Given, AB = AC)∠BFC=∠BEC (each 90∘)Thus, △BFC≅△CEB (ASA rule)Hence, BF=CE (By cpct)AB=AC (Given)Hence, AB−BF=AC−CEAF=AE

In triangle ABC, $A B = A C$ ; $B E$ $⊥$ $A C$ and $C F$ $⊥$ $A B$ .
State whether following statement is true or false
$A F = A E$

True
False

In $△ B F C$ and $△ B E C$ ,
$B C = B C$ (Common)
$∠ F C B = ∠ E B C$ (Given, AB = AC)
$∠ B F C = ∠ B E C$ (each $90^{\circ}$ )
Thus, $△ B F C ≅ △ C E B$ (ASA rule)
Hence, $B F = C E$ (By cpct)
$A B = A C$ (Given)
Hence, $A B - B F = A C - C E$
$A F = A E$