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1 answer:
Answer: C) angle 2 and angle 7
Imagine the parallel lines form the boundaries of river. Angles 3, 4, 5 and 6 are considered interior angles as they are in the river. Angles 1, 2, 7, 8, 9 and 10 are exterior because they're outside the river.
Angles 2 and 7 are on opposite sides of the transversal cut that I've highlighted in red (see diagram below). So that's why they're considered alternate. Combine "exterior" and "alternate" to get "alternate exterior"
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Given that the opposite sides of a parallelogram are congruent, a diagonal
of the parallelogram forms two congruent triangles.
The correct options to complete the proof are;
- <u>Opposite sides of a parallelogram;</u> ABCD is a parallelogram
- <u>Reflexive property of congruency</u>
- <u>SSS</u>
Reasons:
The completed two column proof is presented as follows;
Statement Reason
1. ABCD is a parallelogram 1. Given
2. ≅
and
≅
2. <u>Opposite sides of a parallelogram</u>
3. ≅
3. <u>Reflexive property of congruency</u>
4. ΔABC ≅ ΔCDA 4. <u>SSS</u>
The correct options are therefore;
<u>Opposite sides of a parallelogram;</u> ABCD is a parallelogram
Reflexive property of congruency
SSS;
Reason 2. Opposite sides of a parallelogram, which is based on the
properties of a parallelogram and that ABCD is a parallelogram.
Reason 3. The reflexive property of congruency, states that a side is
congruent to itself.
Reason 4. SSS is an acronym for Side-Side-Side, which is a congruency
postulate that states that if the three sides of one triangle are equal to the
three sides of another triangle, then the two triangles are congruent.
Learn more about parallelograms here:
