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Triangle \(DAC\) is isosceles with congruent sides \(AD\) and \(AC\). Which additional given information is sufficient for showing that triangle \(DBC\) is isosceles? Select all that apply.
Line \(AB\) is an angle bisector of \(DAC\).
Angle \(BAD\) is congruent to angle \(ABC\).
Angle \(BDC\) is congruent to angle \(BCD\).
Angle \(ABD\) is congruent to angle \(ABC\).
Triangle \(DAB\) is congruent to triangle \(CAB\).
Tyler has written an incorrect proof to show that quadrilateral \(ABCD\) is a parallelogram. He knows segments \(AB\) and \(DC\) are congruent. He also knows angles \(ABC\) and \(ADC\) are congruent. Find the mistake in his proof.
Segment \(AC\) is congruent to itself, so triangle \(ABC\) is congruent to triangle \(ADC\) by Side-Angle-Side Triangle Congruence Theorem. Since the triangles are congruent, so are the corresponding parts, and angle \(DAC\) is congruent to \(ACB\). In quadrilateral \(ABCD\), \(AB\) is congruent to \(CD\), and \(AD\) is parallel to \(CB\). Since \(AD\) is parallel to \(CB\), alternate interior angles \(DAC\) and \(BCA\) are congruent. Since alternate interior angles are congruent, \(AB\) must be parallel to \(CD\). Quadrilateral \(ABCD\) must be a parallelogram since both pairs of opposite sides are parallel.
Triangles \(ACD\) and \(BCD\) are isosceles. Angle \(BAC\) has a measure of 18 degrees, and angle \(BDC\) has a measure of 48 degrees. Find the measure of angle \(ABD\).
\(\overline{AD} \cong \overline{AC}\) and \(\overline{BD} \cong \overline{BC}\).
Here are some statements about two zigzags. Put them in order to prove figure \(ABC\) is congruent to figure \(DEF\).
Two figures, A B C and D E F, each composed of two line segments that share an endpoint . A B slants upward and to the left and B C slants upward and to the right. Figure D E F is below and to the right of figure A B C. D E slants upward and to the left and E F slants upward and slightly to the left. B C and E F have one tick mark. A B and D E have two tick marks. Angles B and E marked equal.
Match each statement using only the information shown in the pairs of congruent triangles.
The 2 angles and the included side of one triangle are congruent to 2 angles and the included side of another triangle.
In the two triangles there are 3 pairs of congruent sides.
The 2 sides and the included angle of one triangle are congruent to 2 sides and the included angle of another triangle.
Triangle \(ABC\) is congruent to triangle \(EDF\). So Priya knows that there is a sequence of rigid motions that takes \(ABC\) to \(EDF\).
Select all true statements after the transformations:
Segment \(AB\) coincides with segment \(EF\).
Segment \(BC\) coincides with segment \(DF\).
Segment \(AC\) coincides with segment \(ED\).
Angle \(A\) coincides with angle \(E\).
Angle \(C\) coincides with angle \(F\).