Given that these two triangle are congruent, determine the missing value a.
The corresponding angles of two congruent triangles are congruent. In the first triangle, the angle opposite the side of length 3 is 30^\circ . So its corresponding angle is also 30^\circ .
\widehat{a}=30°
Given that these two triangle are congruent, determine the missing value a.
The corresponding sides of two congruent triangles are congruent. Since we have two right triangles, the hypotenuses are corresponding.
Therefore, the length of the legs of both triangles 3 and 4. The Pythagoras theorem applies and we have:
a=\sqrt{3^2+4^2}=5
a=5
Given that these two triangle are congruent, determine the missing value a.
The corresponding angles of two congruent triangles are congruent. Since the side opposite of \widehat{D} has a length of 17, we can deduce that \widehat{D} is corresponding to \widehat{A}. Therefore, we have:
\widehat{a}=62°
Given that these two triangle are congruent, determine the missing value a.
The corresponding angles of two congruent triangles are congruent. Thus \widehat{a} is congruent to \widehat{A}. We know that:
\widehat{A} + 65^\circ + 35^\circ = 180^\circ
\widehat{A} = 80^\circ
\widehat{a}=80°
Given that these two triangle are congruent, determine the missing value a.
The corresponding sides of two congruent triangles are congruent. Here angles \widehat{F} and \widehat{C} are corresponding so the opposite sides of these angles are also congruent. Thus we have:
a = AB =6
a=6
Given that these two triangle are congruent, determine the missing value a.
The corresponding sides of two congruent triangles are congruent. Here, we can see that \overline{AB} and \overline{DF} are corresponding. Therefore:
a=7
Given that these two triangle are congruent, determine the missing value a.
The corresponding angles of two congruent triangles are congruent. Thus \widehat{a} is congruent to \widehat{B}. We know that:
\widehat{B} + 25^\circ + 30^\circ = 180^\circ
\widehat{B} = 125^\circ
\widehat{a}=125°