Question

practice 3 (from unit 2, lesson 13)
in quadrilateral abcd, ad is congruent to bc, and ad is parallel to bc.
andre has written a proof to show that abcd is a parallelogram. fill in the blanks to complete the proof.
drag and drop the correct answers to the boxes below.
since ad is parallel to, alternate interior angles and are congruent. segment ac is congruent to segment since segments are congruent to themselves. along with the given information that segment ad is congruent to segment bc, triangle adc is congruent to by the triangle congruence. since the triangles are congruent, all pairs of corresponding angles are congruent, so angle dca is congruent to. since those alternate interior angles are congruent, line ab must be parallel to line. since we define a parallelogram as a quadrilateral with both pairs of opposite sides parallel, abcd is a parallelogram.
how did i do?

Explanation:

Step1: Identificar lados paralelos

Como \(AD\parallel BC\), los ángulos internos alternos son \(∠DAC\) y \(∠BCA\).

Step2: Segmentos congruentes

El segmento \(AC\) es congruente consigo mismo (\(AC = AC\)).

Step3: Congruencia de triángulos

Con \(AD = BC\), \(∠DAC=∠BCA\) y \(AC = AC\), el triángulo \(ADC\) es congruente al triángulo \(CBA\) por el criterio \(Side - Angle - Side\).

Step4: Ángulos congruentes

Como los triángulos son congruentes, \(∠DCA = ∠BAC\).

Step5: Lados paralelos

Si \(∠DCA\) y \(∠BAC\) son ángulos internos alternos congruentes, entonces \(AB\parallel CD\).

Answer:

1. \(BC\)
2. \(∠DAC\)
3. \(∠BCA\)
4. \(AC\)
5. \(CBA\)
6. \(Side - Angle - Side\)
7. \(∠BAC\)
8. \(CD\)