{"id":6641,"date":"2021-12-24T08:01:00","date_gmt":"2021-12-24T08:01:00","guid":{"rendered":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/?page_id=6641"},"modified":"2022-01-03T07:21:20","modified_gmt":"2022-01-03T07:21:20","slug":"corresponding-angles-definition-theorems-examples-faq","status":"publish","type":"page","link":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/corresponding-angles-definition-theorems-examples-faq\/","title":{"rendered":"Corresponding Angles: Definition, Theorems, Examples, FAQ"},"content":{"rendered":"

[et_pb_section fb_built=”1″ admin_label=”Section” module_class=”mainsec” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#e0f2fd” z_index=”1″ custom_padding=”5px||5px||true|false” locked=”off” collapsed=”off” global_colors_info=”{}”][et_pb_row column_structure=”3_5,2_5″ custom_padding_last_edited=”on|phone” _builder_version=”4.10.8″ _module_preset=”default” background_color=”#FFFFFF” width=”100%” max_width=”1310px” custom_padding=”|51px|40px|51px|false|true” custom_padding_tablet=”” custom_padding_phone=”|40px|30px|40px|false|true” border_radii=”on|10px|10px|10px|10px” global_colors_info=”{}”][et_pb_column type=”3_5″ admin_label=”Column L” _builder_version=”4.9.10″ _module_preset=”default” global_colors_info=”{}”][et_pb_text admin_label=”Acute Angles
\n” _builder_version=”4.11.3″ _module_preset=”default” header_font=”|700|||||||” header_text_align=”left” header_font_size=”50px” header_line_height=”1.18em” custom_padding=”|0px||4px|false|false” header_font_size_tablet=”” header_font_size_phone=”35px” header_font_size_last_edited=”on|phone” global_colors_info=”{}”]<\/p>\n

Corresponding Angles: Definition, Theorems, Examples, FAQ<\/h1>\n

[\/et_pb_text][et_pb_text admin_label=”Text” _builder_version=”4.13.1″ _module_preset=”default” text_font_size=”16px” header_2_font=”|600|||||||” header_2_text_color=”#a01414″ header_3_font=”|600|||||||” custom_padding=”15px|15px|54px|4px|false|false” global_colors_info=”{}”]<\/p>\n

What Are Corresponding Angles?<\/b><\/h2>\n

According to the definition of corresponding angles, when a third line intersects two lines, the angles formed in matching corners or corresponding positions with the third line are known to be corresponding angles to each other.<\/span><\/p>\n

<\/span><\/p>\n

\"\"<\/span><\/p>\n

<\/span><\/p>\n

In the above diagram:<\/span><\/p>\n

Line 1 and Line 2 are two lines. Line 3 is intersecting Lines 1 and 2.\u00a0<\/span><\/p>\n

The diagram shows that \u22201 and \u22202 have the same relative positions (upper right side angles). Therefore the angles \u22201 and \u22202 are corresponding angles.<\/span><\/p>\n

<\/span><\/p>\n

Types of Corresponding Angles<\/b><\/h2>\n

We learnt that corresponding angles are formed on the opposite side of the transversal. The transversal can intersect either two parallel lines or two non-parallel lines. Hence, there can be two types of corresponding angles:<\/span><\/p>\n

\u00a0<\/b><\/p>\n

Corresponding Angles by Parallel Lines and Transversals<\/b><\/h2>\n

If a transversal (third line) intersects two parallel lines, then the corresponding angles formed are equal in the measurement.\u00a0<\/span><\/p>\n

<\/span><\/p>\n

\"\"<\/span><\/p>\n

<\/span><\/p>\n

In the given diagram, two parallel lines are intersected by a transversal, forming 8 angles with the transversal. In this case, the angles formed by the first line with the transversal are congruent to corresponding angles formed by the second line with the transversal.<\/span><\/span><\/span><\/p>\n

All corresponding angles in the diagram:<\/span><\/p>\n

\u2220p, \u2220w<\/span><\/p>\n

\u2220q, \u2220x<\/span><\/p>\n

\u2220r, \u2220y<\/span><\/p>\n

\u2220s, \u2220z<\/span><\/p>\n

Since the corresponding angles formed by two parallel lines are congruent. So,<\/span><\/p>\n

\u2220p = \u2220w<\/span><\/p>\n

\u2220q = \u2220x<\/span><\/p>\n

\u2220r = \u2220y<\/span><\/p>\n

\u2220s = \u2220z<\/span><\/p>\n

 <\/p>\n

Corresponding Angles by Non-Parallel Lines and Transversals<\/b><\/h2>\n

<\/b><\/p>\n

\"\"<\/b><\/p>\n

<\/span><\/p>\n

If a transversal (third line) intersects any two non-parallel lines, then the corresponding angles formed are not equal in the measurement but are corresponding to each other.<\/span><\/p>\n

 <\/p>\n

Corresponding Angles Theorem<\/b><\/h2>\n

\u201cIf a third-line or a transversal intersects any two parallel lines, then the corresponding angles formed are equal in the measurement\u201d.<\/span><\/p>\n

<\/span><\/p>\n

The Corresponding Angles Converse Theorem<\/b><\/h2>\n

The converse will be the opposite to the above theorem and it says, \u201cIf the corresponding angles in the two intersection regions are equal in the measurement, then the two lines are parallel\u201d.<\/span><\/p>\n

<\/span><\/p>\n

Examples<\/b><\/h2>\n

<\/b><\/p>\n

1. The two corresponding angles formed by a transversal intersecting two parallel lines measure (9x + 6)\u00b0 and 60\u00b0. Find the value of x?<\/strong>
<\/b><\/p>\n

In this case, the two corresponding angles will be congruent.<\/span><\/p>\n

Hence,<\/span><\/p>\n

(9x + 6)\u00b0 = 60\u00b0<\/span><\/p>\n

9x = (60 – 6)\u00b0<\/span><\/p>\n

9x = 54\u00b0<\/span><\/p>\n

x = (54\/9)\u00b0<\/span><\/p>\n

x = 6\u00b0<\/span><\/p>\n

<\/span><\/p>\n

2. If \u2220d = 30\u00b0, find the other angles in the diagram below?<\/strong><\/span><\/p>\n

<\/strong><\/p>\n

<\/span><\/p>\n

\"\"<\/span><\/p>\n

<\/span><\/p>\n

Given, \u2220d = 30\u00b0<\/span><\/p>\n

\u2220d = \u2220b (Vertically opposite angles)<\/span><\/p>\n

So, \u2220b = 30\u00b0<\/span><\/p>\n

\u2220b = \u2220 g = 30\u00b0 (corresponding angles)<\/span><\/p>\n

And, \u2220d = \u2220f (Corresponding angles)<\/span><\/p>\n

So, \u2220f = 30\u00b0<\/span><\/p>\n

\u2220b + \u2220a = 180\u00b0 (supplementary angles)<\/span><\/p>\n

\u2220a+ 30\u00b0 = 180\u00b0<\/span><\/p>\n

\u2220a = 180\u00b0 – 30\u00b0 = 150\u00b0<\/span><\/p>\n

\u2220a = \u2220c (Vertically opposite angles)<\/span><\/p>\n

So, \u2220c = 150\u00b0<\/span><\/p>\n

\u2220 a = \u2220 e (corresponding angles)<\/span><\/p>\n

Hence, \u2220e = 150\u00b0<\/span><\/p>\n

\u00a0And, <\/span>\u2220c = \u2220h = 150\u00b0 (corresponding angles)<\/span><\/p>\n

Therefore, <\/span>\u2220a = 150\u00b0, \u2220b = 30\u00b0 , \u2220c = 150\u00b0 , \u2220e = 150\u00b0 , \u2220f = 30\u00b0 , \u2220g =30\u00b0 and \u2220h = 150\u00b0.\u00a0<\/span><\/span><\/p>\n

[\/et_pb_text][\/et_pb_column][et_pb_column type=”2_5″ module_id=”stickysideR” admin_label=”Column R” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#fdefe0″ custom_padding=”25px|25px|25px|25px|true|true” sticky_position=”top” sticky_offset_top=”-280px” sticky_limit_top=”row” sticky_limit_bottom=”row” sticky_position_tablet=”none” sticky_position_phone=”none” sticky_position_last_edited=”on|desktop” sticky_limit_bottom_tablet=”” sticky_limit_bottom_phone=”” sticky_limit_bottom_last_edited=”on|phone” border_radii=”on|15px|15px|15px|15px” box_shadow_style=”preset3″ global_colors_info=”{}”][et_pb_image src=”https:\/\/eistudymaterial.s3.amazonaws.com\/1080×1080.png” alt=”Free Trial banner” title_text=”Mindspark Free Trial Banner” url=”https:\/\/mindspark.in\/free-trial” align=”center” module_class=”adsimg” _builder_version=”4.11.1″ _module_preset=”default” custom_padding=”||||false|false” border_radii=”on|10px|10px|10px|10px” global_colors_info=”{}” transform_styles__hover_enabled=”on|hover” transform_scale__hover_enabled=”on|hover” transform_translate__hover_enabled=”on|desktop” transform_rotate__hover_enabled=”on|desktop” transform_skew__hover_enabled=”on|desktop” transform_origin__hover_enabled=”on|desktop” transform_scale__hover=”102%|102%”][\/et_pb_image][et_pb_text admin_label=”Explore Other Topics
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Explore Other Topics<\/h1>\n

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\n
Geometry<\/a><\/div>\n
Trigonometry<\/a><\/div>\n
Operations<\/a><\/div>\n
Numbers<\/a><\/div>\n<\/div>\n

[\/et_pb_text][et_pb_text admin_label=”Related Concepts
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Related Concepts<\/h1>\n

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\n
Adjacent Angles<\/a><\/div>\n
Reflex Angle<\/a><\/div>\n
Vertically Opposite Angles<\/a><\/div>\n<\/div>\n

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Frequently Asked Questions\u00a0<\/span><\/span><\/h1>\n
    <\/ol>\n

    Q1. Are all Corresponding Angles Equal?
    <\/strong><\/h3>\n

    Ans: <\/strong>No, all corresponding angles are not equal. If a third line or a transversal intersects any two parallel lines, then the corresponding angles formed are equal in the measurement.
    <\/span><\/span><\/p>\n

    Q2. What are Corresponding Angles?
    <\/strong><\/h3>\n

    Ans: <\/strong>According to geometry, when a third line or transversal, of the above theorem. It intersects two lines, the angles formed in matching corners or corresponding positions with the transversal are known to be corresponding angles to each other.<\/strong><\/p>\n

    Q3. What are the theorems for corresponding angles?<\/strong><\/h3>\n

    Ans: <\/strong>The theorem for corresponding angles says \u201cThe corresponding angles are equal if the transversal intersects two parallel lines.\u201d Its converse theorem says \u201cif a transversal intersects two parallel lines, the corresponding angles will always be equal.\u201d<\/strong><\/strong><\/p>\n

    [\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"

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