Question

geometría 1, lección 1: vocabularios - tarea p , nombre: __
do you agree or disagree with the statement? if not, please identify the error and make a correction.

statements:

1. an isosceles triangle has 3 congruent sides.
2. equilateral triangles have only 2 congruent sides.
3. parallel lines never intersect.
4. if two lines intersect, then they are perpendicular.
5. the angle is more than 90 degrees.
6. two right angles next to each other, you can have a straight angle.
7. complementary angles are two angles that add up to 90 degrees.
8. the midpoint of a segment divides the segment into 2 equal halves.
9. the median passes through the midpoint of a side of a triangle.
10. the two legs of a right angle are not perpendicular.
11. obtuse angle is more than 90 degrees and less than 180 degrees.
12. the segment bisector makes two congruent angles.
13. congruent angles are angles with the same length.

one questions i have is

Answer:

To solve this, we analyze each statement based on geometric definitions:

1. An isosceles triangle has 3 congruent sides.

• Definition: Isosceles triangles have at least 2 congruent sides (equilateral triangles, with 3 congruent sides, are a special case of isosceles, but the statement incorrectly claims "3" as the only case).
• Mark: $\boldsymbol{\times}$
• Correction: An isosceles triangle has at least 2 congruent sides (or: A triangle with 3 congruent sides is equilateral).

2. Equilateral triangles have only 2 congruent sides.

• Definition: Equilateral triangles have 3 congruent sides.
• Mark: $\boldsymbol{\times}$
• Correction: Equilateral triangles have 3 congruent sides.

3. Parallel lines never intersect.

• Definition: Parallel lines (in a plane) are lines that never intersect.
• Mark: $\boldsymbol{\checkmark}$

4. If two lines intersect, then they are perpendicular.

• Definition: Perpendicular lines intersect at a right angle ($90^\circ$), but not all intersecting lines are perpendicular (e.g., lines intersecting at $30^\circ$).
• Mark: $\boldsymbol{\times}$
• Correction: If two lines intersect at a right angle, then they are perpendicular (or: Not all intersecting lines are perpendicular).

5. The angle is more than 90 degrees.

• Issue: The statement is too vague (no specific angle). Angles can be acute ($<90^\circ$), right ($=90^\circ$), obtuse ($>90^\circ$), or straight ($=180^\circ$), etc.
• Mark: $\boldsymbol{\times}$
• Correction: Specify the angle (e.g., "An obtuse angle is more than 90 degrees").

6. Two right angles next to each other, you can have a straight angle.

• Calculation: A right angle is $90^\circ$, so $90^\circ + 90^\circ = 180^\circ$ (a straight angle).
• Mark: $\boldsymbol{\checkmark}$

7. Complementary angles are two angles that add up to 90 degrees.

• Definition: This matches the definition of complementary angles.
• Mark: $\boldsymbol{\checkmark}$

8. The midpoint of a segment divides the segment into 2 equal halves.

• Definition: A midpoint splits a segment into two congruent (equal-length) parts.
• Mark: $\boldsymbol{\checkmark}$

9. The median passes through the midpoint of a side of a triangle.

• Definition: A median of a triangle connects a vertex to the midpoint of the opposite side, so it passes through the midpoint.
• Mark: $\boldsymbol{\checkmark}$

10. The two legs of a right angle are NOT perpendicular.

• Definition: In a right angle, the two legs (sides forming the angle) are perpendicular (they meet at $90^\circ$).
• Mark: $\boldsymbol{\times}$
• Correction: The two legs of a right angle ARE perpendicular.

11. Obtuse angle is more than 90 degrees and less than 180 degrees.

• Definition: This matches the definition of an obtuse angle.
• Mark: $\boldsymbol{\checkmark}$

12. The segment bisector makes two congruent angles.

• Definition: A segment bisector (a line/segment/ray that bisects a segment) splits the segment into two equal parts, but it does not necessarily form angles (unless it is an angle bisector). The statement confuses "segment bisector" with "angle bisector."
• Mark: $\boldsymbol{\times}$
• Correction: An angle bisector makes two congruent angles (or: A segment bisector divides a segment into two congruent segments).

13. Congruent angles are angles with the same length.

• Definition: Congruent angles have the same measure (in degrees), not "length" (length applies to segments).
• Mark: $\boldsymbol{\times}$
• Correction: Congruent angles are angles with the same measure.

Final Table (Marks + Corrections):

Statements	$\boldsymbol{\checkmark}$	$\boldsymbol{\times}$	Corrections (if $\boldsymbol{\times}$)
2. Equilateral triangles have only 2 congruent sides.		$\times$	Equilateral triangles have 3 congruent sides.
3. Parallel lines never intersect.	$\checkmark$		–
4. If two lines intersect, then they are perpendicular.		$\times$	If two lines intersect at a right angle, then they are perpendicular.
5. The angle is more than 90 degrees.		$\times$	Specify the angle (e.g., "An obtuse angle is more than 90 degrees").
6. Two right angles next to each other, you can have a straight angle.	$\checkmark$		–
7. Complementary angles are two angles that add up to 90 degrees.	$\checkmark$		–
8. The midpoint of a segment divides the segment into 2 equal halves.	$\checkmark$		–
9. The median passes through the midpoint of a side of a triangle.	$\checkmark$		–
10. The two legs of a right angle are NOT perpendicular.		$\times$	The two legs of a right angle ARE perpendicular.
11. Obtuse angle is more than 90 degrees and less than 180 degrees.	$\checkmark$		–
12. The segment bisector makes two congruent angles.		$\times$	An angle bisector makes two congruent angles.
13. Congruent angles are angles with the same length.		$\times$	Congruent angles are angles with the same measure.

(Note: For the "One question I have is" section, a student might ask, e.g., "What’s the difference between a segment bisector and an angle bisector?" or "Why is an equilateral triangle also isosceles?")