what shape in this lesson can be used to prove statements about triangles?
Multiple-Choice Items:
1. The definition of coinciding triangles states
| A | that all pairs of corresponding sides are congruent. |
| B | that all pairs of corresponding angles are coinciding. |
| C | that one pair of corresponding sides and one pair of respective angles are coinciding. |
| D | that all pairs of corresponding sides and all pairs of respective angles are congruent. |
two. Given two triangles, you know that they have two pairs of respective, congruent angles. Based on this, what can you conclude about the two triangles?
| A | The 2 triangles are congruent, just not necessarily like. |
| B | The 2 triangles are similar, but not necessarily congruent. |
| C | The two triangles are both congruent and similar. |
| D | You cannot conclude anything nearly the congruence or similarity of the two triangles. |
3. Which statement is true nigh two like triangles?
| A | They always have equal areas. |
| B | They always have equal perimeters. |
| C | They are ever congruent. |
| D | They are sometimes congruent. |
Utilize the post-obit information for items 4–half-dozen:
Triangle DEF (ΔDEF) is congruent to ΔNOM.
four. Which side in ΔNOM corresponds to?
v. Which bending in ΔNOM corresponds to ÐFED?
6. In ΔDEF,
is half dozen cm and
is five cm. What is the length of 
?
| A | 1 cm |
| B | 5 cm |
| C | 6 cm |
| D | 11 cm |
In items seven–nine, utilise the following triangles:
seven. Which theorem or postulate can be used to evidence that the two triangles are similar?
| A | the definition of similar triangles |
| B | SSS |
| C | AA |
| D | SAS |
8. What is the length of 
?
| A | four cm |
| B | 13 cm |
| C | sixteen cm |
| D | twoscore cm |
9. What is the scale cistron that compares ΔABC to ΔDEF?
Multiple-Choice Answer Key:
| 1. D | 2. B | 3. D | 4. C | 5. A |
| half dozen. B | 7. C | 8. C | 9. A |
Short-Reply Items:
In items 10 and 11 below, utilise the following data to answer the questions:
At three p.grand., Chuck, who is 6 feet tall, goes outside. He measures his shadow and finds that his shadow is ii anxiety long. He wants to measure the height of a nearby building that is casting a shadow that is 140 anxiety long.
x. Draw two triangles to illustrate the situation. Clearly characterization all known parts of each triangle.
11. How tall is the nearby building? Show your work and list any theorems or postulates that you used to find your respond.
12. How would you decide if two figures are congruent? Be certain to include your understanding of congruency, diagrams and what they hateful, and land the advisable theorems that support your reasoning.
| A | Draw two congruent figures. |
| B | Definition congruency equally it applies to your examples. |
| C | Use supporting theorems and explicate how they apply to your examples. |
13. List three ways to prove triangles are congruent. Explicate the reasoning that supports your answers.
Short-Reply Primal and Scoring Rubrics:
In items 10 and eleven below, use the following information to answer the questions:
At 3 p.k., Chuck, who is 6 feet tall, goes outside. He measures his shadow and finds that his shadow is 2 feet long. He wants to measure the peak of a nearby edifice that is casting a shadow that is 140 feet long.
x. Draw two triangles to illustrate the state of affairs. Clearly label all known parts of each triangle.
The student should draw 2 similar right triangles, one with the peak labeled
6 anxiety, and the other leg labeled ii feet, and a correct-angle mark; the other triangle should have the shorter leg labeled 140 anxiety and too take a right-angle mark.
| Points | Description |
| 5 | The student's reply includes:
|
| iv | The student's reply includes 4 of the five requirements. |
| three | The student'due south respond includes three of the five requirements. |
| ii | The educatee's answer includes two of the five requirements. |
| 1 | The pupil's answer includes one of the five requirements. |
| 0 | The student's answer does not include any of the v requirements. |
11. How alpine is the nearby edifice? Show your piece of work and list whatever theorems or postulates that you used to find your reply.
Using AA Similarity and the proportion 
, the height of the edifice is 420 anxiety.
| Points | Clarification |
| iii | The student:
|
| ii | The pupil'south respond includes 2 of the 3 requirements. |
| one | The student'southward answer includes one of the three requirements. |
| 0 | The student'southward respond does non include any of the 3 requirements. |
12. How would you decide if two figures are congruent? Be certain to include the definition of congruency, diagrams and land theorems to support your reply.
| A | Describe two coinciding figures. |
| B | Definition of congruent |
| C | Supporting theorems |
Congruency is determined past the definition (proving all pairs of corresponding parts are congruent) using SAS, AAS, or SSS. Congruency means the sides and angles are exactly the aforementioned. Students should draw any diagrams demonstrating the figures are equal and congruent.
thirteen. Listing 3 ways to evidence triangles are congruent.
Students can receive up to iii points, 1 point for each valid method to show triangle congruence.
Performance Assessment:
- Are the 2 triangles congruent, similar, or neither? If they are congruent or similar, write a congruence argument for the two triangles. If they are neither congruent nor similar, explain why.
- Determine the value of 10 and y.
- Make up one's mind the values of the two missing angles (one in each triangle).
- Are the two triangles coinciding, similar, or neither? If they are congruent or similar, write a congruence statement for the two triangles. If they are neither congruent nor similar, explain why.
Operation Assessment Respond Key and Scoring Rubric:
The two triangles are like. The similarity statement is "ΔABC is similar to ΔDEF."
- Determine the value of 10 and y.
x = 12 cm
y = 6.5 cm
3. Determine the values of the 2 missing angles (one in each triangle).
The missing angle in each triangle is 23 degrees.
| Points | Description |
| iv | The student's answer includes:
|
| 3 |
|
| ii |
|
| 1 |
|
| 0 |
|
Source: https://www.pdesas.org/ContentWeb/Content/Content/21054/Unit%20Plan
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