Geometric Twins

Which criterion is used to show two triangles are congruent if three sides of one are equal to three sides of another?

If $\angle P \cong \angle Q$, then the measure of $\angle P$ and $\angle Q$ is _____.

Congruent triangles have _____ areas.

If $\Delta ABC$ is an isosceles triangle with $AB = AC$, and $AD$ is the bisector of $\angle A$, then $\Delta ABD \cong \Delta ACD$ by _____ rule.

Two triangles are congruent if they are ____________ of each other.

If $\triangle PQR \cong \triangle EFD$, then $\angle Q$ is equal to ____________.

For two triangles to be congruent by SSS, how many pairs of corresponding sides must be equal?

In $\triangle ABC$ and $\triangle PQR$, $AB = PQ$, $BC = QR$, and $\angle B = \angle Q$. If $\angle A = 2x + 20^{\circ}$ and $\angle P = 3x - 10^{\circ}$, find $x$.

Two isosceles triangles have equal vertical angles. What additional condition is needed for them to be congruent?

If two triangles have three angles of one equal to three angles of the other, they are:

In the given figure, triangle $ABC$ and triangle $PQR$ are shown with their corresponding equal parts marked. Given that $AB = PQ$, $BC = QR$, and $\angle B = \angle Q$, which congruence criterion proves that $\triangle ABC \cong \triangle PQR$?

In the figure, which criterion proves $\triangle ABD \cong \triangle ACD$ if $BD = CD$ and $AD$ is perpendicular to $BC$?

If $\triangle PQR \cong \triangle ABC$, then $\angle Q$ is equal to:

Two line segments are congruent if they have the same:

In the figure, if $AD = BC$ and $\angle DAB = \angle CBA$, then $\triangle ABD \cong \triangle BAC$ by:

Two squares are congruent if they have the same:

If $\triangle ABC \cong \triangle PQR$, $AB = 5\text{ cm}$, $BC = 6\text{ cm}$ and $AC = 7\text{ cm}$, then the length of $QR$ is:

If $\triangle ABC \cong \triangle PQR$ under the correspondence $ABC \leftrightarrow RQP$, which side of $\triangle PQR$ is equal to $BC$?

In $\triangle ABC$, the altitudes $BE$ and $CF$ are equal. Using the RHS congruence rule, which pair of triangles is proved congruent to show $\triangle ABC$ is isosceles?

In the given figure, $O$ is the midpoint of both $AB$ and $CD$. To prove $\triangle AOC \cong \triangle BOD$, which congruence rule is applied?

In the given isosceles triangle $ABC$, the side $AB$ is equal to side $AC$. If the measure of the vertex angle $\angle A$ is $40^{\circ}$, what is the measure of the base angle $\angle B$?

True or False: An equilateral triangle is also an isosceles triangle.

In an isosceles triangle, if the vertex angle is $60^\circ$, what is the triangle specifically called?

If the three sides of a triangle are $7\text{ cm}$, $7\text{ cm}$, and $7\text{ cm}$, what is the sum of any two of its angles?

If $\triangle ABC$ is equilateral and a line $DE$ is drawn parallel to $BC$ intersecting $AB$ and $AC$, what type of triangle is $\triangle ADE$?

In an isosceles triangle, the base angle is $15^\circ$ less than the vertex angle. Find the vertex angle.

In an equilateral triangle $ABC$, $D$ is a point on $BC$ such that $AD \perp BC$. What is the measure of $\angle BAD$?

An isosceles triangle $\Delta LMN$ has $LM = LN$. A line segment $LP$ is drawn such that $P$ lies on $MN$ and $\Delta LMP$ is also an isosceles triangle with $LM = MP$. If $\angle MLN = 100^{\circ}$, find the measure of $\angle LPN$.

Two equilateral triangles, $\Delta ABC$ and $\Delta DCE$, are placed side by side such that $B, C,$ and $E$ are collinear. What is the measure of $\angle ACD$?

A compass needle is shaped like a very thin isosceles triangle. If the narrow vertex angle is $2^{\circ}$, and the needle is split exactly down the middle from the vertex to the base, what are the angles of the two new right-angled triangles formed?